Chapter 10Resource Masters
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Permission isgranted to reproduce the material contained herein on the condition that suchmaterial be reproduced only for classroom use; be provided to students, teachers,and families without charge; and be used solely in conjunction with GlencoeCalifornia Mathematics, Grade 6. Any other reproduction, for use or sale, isprohibited without prior written permission of the publisher.
Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240
ISBN: 978-0-07-878305-0MHID: 0-07-878305-4 CAGR6 CRM10
Printed in the United States of America
4 5 6 7 8 9 10 MAL 14 13 12 11 10 09
Consumable Workbooks Many of the worksheets contained in the Chapter Resource Masters
booklets are available as consumable workbooks in both English and Spanish.
MHID ISBNStudy Guide and Intervention Workbook 0-07-878871-4 978-0-07-878871-0
Skills Practice Workbook 0-07-878873-0 978-0-07-878873-4
Practice Workbook 0-07-878875-7 978-0-07-878875-8
Word Problem Practice Workbook 0-07-878877-3 978-0-07-878877-2
Spanish VersionsStudy Guide and Intervention Workbook 0-07-878872-2 978-0-07-878872-7Skills Practice Workbook 0-07-878874-9 978-0-07-878874-1Practice Workbook 0-07-878876-5 978-0-07-878876-5Word Problem Practice Workbook 0-07-878878-1 978-0-07-878878-9
Answers for Workbooks The answers for Chapter 10 of these workbooks can be found in the
back of this Chapter Resource Masters booklet.
StudentWorks Plus™ This CD-ROM includes the entire Student Edition test along with the
English workbooks listed above.
TeacherWorks Plus™ All of the materials found in this booklet are included for viewing,
printing, and editing in this CD-ROM.
Spanish Assessment Masters MHID: 0-07-878879-X ISBN: 978-0-07-878879-6
These masters contain a Spanish version of Chapter 10 Test Form 2A and Form 2C.
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Teacher’s Guide to Using the Chapter 10 Resource Masters .........................................iv
Chapter Resources Chapter 10 Student-Built Glossary ....................1Chapter 10 Family Letter (English) ....................3Chapter 10 Family Activity (English) ..................4Chapter 10 Family Letter (Spanish) ...................5Chapter 10 Family Activity (Spanish).................6Chapter 10 Anticipation Guide (English)............7Chapter 10 Anticipation Guide (Spanish) ..........8
Lesson 10-1 Angle RelationshipsLesson Reading Guide ......................................9Study Guide and Intervention ..........................10Skills Practice...................................................11Practice ............................................................12Word Problem Practice ....................................13Enrichment .......................................................14
Lesson 10-2 Complementary andSupplementary AnglesLesson Reading Guide ....................................15Study Guide and Intervention ..........................16Skills Practice...................................................17Practice ............................................................18Word Problem Practice ....................................19Enrichment .......................................................20
Lesson 10-3 Statistics: DisplayData in a Circle GraphLesson Reading Guide ....................................21Study Guide and Intervention ..........................22Skills Practice...................................................23Practice ............................................................24Word Problem Practice ....................................25Enrichment .......................................................26TI-73 Activity ....................................................27
Lesson 10-4 TrianglesLesson Reading Guide ....................................28Study Guide and Intervention ..........................29Skills Practice...................................................30Practice ............................................................31Word Problem Practice ....................................32Enrichment .......................................................33
Lesson 10-5 Problem-SolvingInvestigation: Use LogicalReasoningStudy Guide and Intervention ..........................34Skills Practice...................................................35Practice ............................................................36Word Problem Practice ....................................37
Lesson 10-6 QuadrilateralsLesson Reading Guide ....................................38Study Guide and Intervention ..........................39Skills Practice...................................................40Practice ............................................................41Word Problem Practice ....................................42Enrichment .......................................................43
Lesson 10-7 Similar FiguresLesson Reading Guide ....................................44Study Guide and Intervention ..........................45Skills Practice...................................................46Practice ............................................................47Word Problem Practice ....................................48Enrichment .......................................................49
Lesson 10-8 Polygons andTessellationsLesson Reading Guide ....................................50Study Guide and Intervention ..........................51Skills Practice...................................................52Practice ............................................................53Word Problem Practice ....................................54Enrichment .......................................................55TI-73 Activity ....................................................56
Lesson 10-9 TranslationsLesson Reading Guide ....................................57Study Guide and Intervention ..........................58Skills Practice...................................................59Practice ............................................................60Word Problem Practice ....................................61Enrichment .......................................................62Spreadsheet Activity ........................................63
Lesson 10-10 ReflectionsLesson Reading Guide ....................................64Study Guide and Intervention ..........................65Skills Practice...................................................66Practice ............................................................67Word Problem Practice ....................................68Enrichment .......................................................69TI-73 Activity ....................................................70
Chapter 10 AssessmentStudent Recording Sheet ................................71Rubric for Scoring Pre-AP................................72Chapter 10 Quizzes 1 and 2 ............................73Chapter 10 Quizzes 3 and 4 ............................74Chapter 10 Mid-Chapter Test ...........................75Chapter 10 Vocabulary Test .............................76Chapter 10 Test, Form 1 ..................................77Chapter 10 Test, Form 2A................................79Chapter 10 Test, Form 2B................................81Chapter 10 Test, Form 2C................................83Chapter 10 Test, Form 2D................................85Chapter 10 Test, Form 3 ..................................87Chapter 10 Extended-Response Test ..............89Chapter 10 Standardized Test Practice............90
Answers..................................................A1–A41
Contents
iv
Teacher’s Guide to Using the Chapter 10 Resource Masters
The Chapter 10 Resource Masters includes the core materials needed for Chapter 10. Thesematerials include worksheets, extensions, and assessment options. The answers for thesepages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing on theTeacherWorks Plus™ CD-ROM.
Chapter ResourcesStudent-Built Glossary (pages 1–2) Thesemasters are a student study tool thatpresents up to twenty of the key vocabularyterms from the chapter. Students are torecord definitions and/or examples for eachterm. You may suggest that studentshighlight or star the terms with which theyare not familiar. Give this to students beforebeginning Lesson 10-1. Encourage them toadd these pages to their mathematics studynotebooks. Remind them to complete theappropriate words as they study each lesson.
Family Letter and Family Activity(pages 3–6) The letter informs yourstudents’ families of the mathematics theywill be learning in this chapter. The familyactivity helps them to practice problems thatare similar to those on the state test. A fullsolution for each problem is included.Spanish versions of these pages are alsoincluded. Give these to students to takehome before beginning the chapter.
Anticipation Guide (pages 7–8) Thismaster, presented in both English andSpanish, is a survey used before beginningthe chapter to pinpoint what students mayor may not know about the concepts in thechapter. Students will revisit this surveyafter they complete the chapter to see iftheir perceptions have changed.
Lesson ResourcesLesson Reading Guide Get Ready for theLesson reiterates the questions from thebeginning of the Student Edition lesson.Read the Lesson asks students to interpretthe context of and relationships amongterms in the lesson. Finally, RememberWhat You Learned asks students tosummarize what they have learned usingvarious representation techniques. Use as astudy tool for note taking or as an informalreading assignment. It is also a helpful toolfor ELL (English Language Learners).
Study Guide and Intervention Thismaster provides vocabulary, key concepts,additional worked-out examples and CheckYour Progress exercises to use as areteaching activity. It can also be used inconjunction with the Student Edition as aninstructional tool for students who havebeen absent.
Skills Practice This master focuses moreon the computational nature of the lesson.Use as an additional practice option or ashomework for second-day teaching of thelesson.
Practice This master closely follows thetypes of problems found in the Exercisessection of the Student Edition and includesword problems. Use as an additionalpractice option or as homework for second-day teaching of the lesson.
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Word Problem Practice This masterincludes additional practice in solving wordproblems that apply the concepts of thelesson. Use as an additional practice or ashomework for second-day teaching of thelesson.
Enrichment These activities may extendthe concepts of the lesson, offer a historicalor multicultural look at the concepts, orwiden students’ perspectives on themathematics they are learning. They arewritten for use with all levels of students.
Graphing Calculator, ScientificCalculator, or Spreadsheet ActivitiesThese activities present ways in whichtechnology can be used with the concepts insome lessons of this chapter. Use as analternative approach to some concepts or asan integral part of your lesson presentation.
Assessment OptionsThe assessment masters in the Chapter 10Resource Masters offer a wide range ofassessment tools for formative (monitoring)assessment and summative (final) assessment.
Student Recording Sheet This mastercorresponds with the standardized testpractice at the end of the chapter.
Pre-AP Rubric This master providesinformation for teachers and students onhow to assess performance on open-endedquestions.
Quizzes Four free-response quizzes offerassessment at appropriate intervals in thechapter.
Mid-Chapter Test This 1-page testprovides an option to assess the first half ofthe chapter. It parallels the timing of theMid-Chapter Quiz in the Student Editionand includes both multiple-choice and free-response questions.
Vocabulary Test This test is suitable forall students. It includes a list of vocabularywords and 10 questions to assess students’knowledge of those words. This can also beused in conjunction with one of the leveledchapter tests.
Leveled Chapter Tests• Form 1 contains multiple-choice questions
and is intended for use with below gradelevel students.
• Forms 2A and 2B contain multiple-choicequestions aimed at on grade levelstudents. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D contain free-responsequestions aimed at on grade levelstudents. These tests are similar in formatto offer comparable testing situations.
• Form 3 is a free-response test for use withabove grade level students.
All of the above mentioned tests include afree-response Bonus question.
Extended-Response Test Performanceassessment tasks are suitable for allstudents. Sample answers and a scoringrubric are included for evaluation.
Standardized Test Practice These threepages are cumulative in nature. It includesthree parts: multiple-choice questions withbubble-in answer format, griddablequestions with answer grids, and short-answer free-response questions.
Answers• The answers for the Anticipation Guide
and Lesson Resources are provided asreduced pages with answers appearing in red.
• Full-size answer keys are provided for theassessment masters.
Chapter 10 1 Glencoe California Mathematics, Grade 6
NAME ________________________________________ DATE ______________ PERIOD _____
Student-Built Glossary
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esThis is an alphabetical list of new vocabulary terms you will learn inChapter 10. As you study the chapter, complete each term’s definitionor description. Remember to add the page number where you foundthe term. Add this page to your math study notebook to reviewvocabulary at the end of the chapter.
10
Vocabulary TermFound
Definition/Description/Exampleon Page
acute angle
complementary angles
congruent angles
congruent figures
line of reflection
line of symmetry
line symmetry
obtuse angle
parallelogram
polygon
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Chapter 10 2 Glencoe California Mathematics, Grade 6
Vocabulary TermFound
Definition/Description/Exampleon Page
quadrilateral KWAH-druh-LA-tuh-ruhl
reflection
rhombus RAHM-buhs
similar figures
straight angle
supplementary angles
tessellation
transformation
translation
trapezoid TRA-puh-ZOYD
vertex
NAME ________________________________________ DATE ______________ PERIOD _____
Student-Built Glossary (continued)10
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Family LetterNAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 3 Glencoe California Mathematics, Grade 6
Dear Parent or Guardian:
Geometric figures can be found in all kinds of places. Wallpaper
and tile often contain geometric patterns. Traffic signs are
created in the shapes of various types of polygons. Applying
geometric concepts to the real world can help us solve many
types of problems.
In Chapter 10, Geometry: Polygons, your child will learn about
angles, circle graphs, polygons, similar figures, tessellations,
translations, and reflections. Your child will also learn to use logical
reasoning to solve problems. In the study of this chapter, your child
will complete a variety of daily classroom assignments and activities
and possibly produce a chapter project.
By signing this letter and returning it with your child, you agree
to encourage your child by getting involved. Enclosed is an
activity you can do with your child that practices how the math
we will be learning in Chapter 10 might be tested. You may
also wish to log on to ca.gr6math.com for self-check quizzes
and other study help. If you have any questions or comments,
feel free to contact me at school.
Sincerely,
Signature of Parent or Guardian ______________________________________ Date ________
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Family ActivityStandards Practice
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 4 Glencoe California Mathematics, Grade 6
10
Fold the page along the dashed line. Work each problem on another piece of paper.Then unfold the page to check your work.
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1. On the coordinate axis shown below, thegeometric shape has been transformedin some way.
What word best describes thetransformation that has taken place?
A rotationB translationC reflectionD dilation
Fold here.
Solution
1. Hint: An object that has been rotated hasbeen turned around a point. An objectthat has been translated has been movedin its current form to different coordinatesin the plane. An object that has beenreflected will be a mirror image of theoriginal object over a line of reflection. Adilation results in a change in size fromthe original object.
The object has not been turned, so it isnot a rotation. The object is orienteddifferently than originally, so it cannotbe a translation. The object's size didnot change, so it cannot be a dilation.
The object is a mirror image of itself onthe other side of the x-axis, so thetransformation is a reflection.
The answer is C.
2. The following triangles are similar.
Which of the following is not true aboutsimilar figures?
A Similar figures have equalcorresponding angles.
B Similar figures have proportionalcorresponding side lengths.
C Similar figures do not have to haveproportional corresponding sidelengths.
D Similar figures are the same shapebut may be a different size.
Solution
2. Hint: Similar triangles have the sameshape and their sizes are proportional.
When two figures are similar, they arethe same shape, their correspondingsides are proportional, and correspondingangles are equal. Based on the definitionof similar figures, choices A, B, and D arealso true.
Choice C directly contradicts thedefinition of similar figures and is not true.
The answer is C.
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Carta a la familiaNOMBRE ______________________________________ FECHA ____________ PERÍODO ___
Capítulo 10 5 Glencoe California Mathematics, Grade 6
Estimado padre o apoderado:
Hay figuras geométricas por doquier. El papel tapiz y las
baldosas contienen a menudo patrones geométricos. Las señales
de tránsito se fabrican en forma de varios tipos de polígonos. La
aplicación de conceptos geométricos al mundo real puede
ayudarnos a resolver muchos tipos de problemas.
En el Capítulo 10, Geometría: Polígonoss, su hijo(a) aprenderá
sobre ángulos, gráficas circulares, polígonos, figuras semejantes,
teselados, traslaciones y reflexiones. Su hijo(a) también aprenderá
a usar el razonamiento lógico para resolver problemas. En el estu-
dio de este capítulo, su hijo(a) completará una variedad de tareas
y actividades diarias y es posible que trabaje en un proyecto del
capítulo.
Al firmar esta carta y devolverla con su hijo(a), usted se com-
promete a ayudarlo(a) a participar en su aprendizaje. Junto con
esta carta, va incluida una actividad que puede realizar con
él(ella) y la cual practica lo que podrían encontrar en las prue-
bas de los conceptos matemáticos que aprenderán en el
Capítulo 10. Además, visiten ca.gr6math.com para ver auto-
controles y otras ayudas para el estudio. Si tiene cualquier pre-
gunta o comentario, por favor contácteme en la escuela.
Cordialmente,
Firma del padre o apoderado ________________________________________ Fecha ______
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Actividad en familiaPráctica de estándares
NOMBRE ______________________________________ FECHA ____________ PERÍODO ___
Capítulo 10 6 Glencoe California Mathematics, Grade 6
1. En el plano de coordenadas siguiente, laforma geométrica se transformó dealguna manera.
¿Qué palabra describe mejor estatransformación?
A rotaciónB traslaciónC reflexiónD dilatación
Doblen aquí.
Solución
1. Ayuda: Un objeto que se ha rotado esaquél que se hace girar alrededor de unpunto. Un objeto trasladado se mueve ensu forma actual a diferentes coordenadasen el plano. Un objeto reflejado es unaimagen especular del objeto original sobreun eje de reflexión. Una dilación resulta enel cambio de tamaño del objeto original.
El objeto no se giró, de modo que no esuna rotación. El objeto se orienta demanera distinta a la original, por eso nopuede ser una traslación. Su tamaño nocambió, entonces no puede ser unadilatación.
El objeto es una imagen especular de símismo del otro lado del eje x, de modoque la transformación es una reflexión.
La respuesta es C.
2. Los siguientes triángulos son semejantes.
¿Cuál de los siguientes no cierto encuanto a figuras semejantes?
A Éstas tienen ángulos correspondien-tes iguales.
B Éstas tienen longitudes lateralescorrespondientes proporcionales.
C Éstas no necesitan tener longitudeslaterales correspondientesproporcionales.
D Éstas tienen la misma forma peropueden tener un tamaño distinto.
Solución
2. Ayuda: Los triángulos semejantes tienenla misma forma y sus tamaños sonproporcionales.
Dos figuras son semejantes cuandotienen la misma forma, son proporciona-les sus lados correspondientes y soniguales sus ángulos correspondientes. Enbase a la definición de figuras semejan-tes, las opciones A, B y D también sonciertas.
La opción C contradice directamente ladefinición de figuras semejantes y no esverdadera.
La respuesta es C.
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Doblen la página a lo largo de las líneas punteadas. Resuelvan cada problema en otra hoja de papel. Luego, desdoblen la página y revisen las respuestas.
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NAME ________________________________________ DATE ______________ PERIOD _____
Anticipation GuideGeometry: Polygons
Chapter 10 7 Glencoe California Mathematics, Grade 6
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Step 2
Step 1
STEP 1 Statement STEP 2A, D, or NS A or D
1. The point where the sides of an angle meet is called the vertex.
2. An obtuse angle has a measure less than 90°.3. Two angles are complementary if the sum of their measures
is 180°.4. The percents in a circle graph total 100% and the angle
measures will total 360°.5. The sum of the measures of the angles in a triangle is 360°.6. A triangle is classified as obtuse if one angle in the triangle
is obtuse.7. All rectangles are quadrilaterals, but not all quadrilaterals
are rectangles.8. Figures that are the same shape and size are called similar
figures.9. If two figures are similar, then the corresponding angles are
congruent.10. A polygon is a two-dimensional figure with five sides.11. After a figure is translated, the resulting figure is the same
size and shape as the original.12. Only figures with at least one line of symmetry can be
transformed by a reflection.
Before you begin Chapter 10
• Read each statement.
• Decide whether you Agree (A) or Disagree (D) with the statement.
• Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).
After you complete Chapter 10
• Reread each statement and complete the last column by entering an A or a D.
• Did any of your opinions about the statements change from the first column?
• For those statements that you mark with a D, use a piece of paper to write an example of why you disagree.
10
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NOMBRE ______________________________________ FECHA ____________ PERÍODO ___
Ejercicios preparatoriosGeometría: Polígonos
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PASO 2
Antes de comenzar el Capítulo 10
• Lee cada enunciado.
• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.
• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta,escribe NS (No estoy seguro(a).
Después de completar el Capítulo 10
• Vuelve a leer cada enunciado y completa la última columna con una A o una D.
• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?
• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con losenunciados que marcaste con una D.
PASO 1
PASO 1 PASO 2A, D o NS
EnunciadoA o D
1. El punto donde se encuentran los lados de un ángulo se llama vértice.
2. Un ángulo obtuso mide menos que 90°.3. Dos ángulos son complementarios si la suma de sus medidas
es 180°.4. Los porcentajes en una gráfica circular totalizan 100% y las
medidas angulares totalizan 360°.5. La suma de las medidas de los ángulos de un triángulo es 360°.6. Un triángulo se clasifica como obtusángulo si uno de sus
ángulos es obtuso.7. Todos los rectángulos son cuadriláteros, pero no todos los
cuadriláteros son rectángulos.8. Las figuras que son iguales en forma y tamaño se llaman
figuras semejantes.9. Si dos figuras son semejantes, entonces sus ángulos
correspondientes son congruentes.10. Un polígono es una figura bidimensional con cinco lados.11. Después de trasladar una figura, la figura resultante es igual
en tamaño y forma a la original.12. Sólo figuras con por lo menos un eje de simetría pueden
transformarse mediante reflexión.
Capítulo 10 8 Glencoe California Mathematics, Grade 6
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Chapter 10 9 Glencoe California Mathematics, Grade 6
Lesson Reading GuideAngle Relationships
Get Ready for the LessonRead the introduction at the top of page 510 in your textbook. Writeyour answers below.
1. Name other times in which the hands of a clock form angles less than 90°, equal to 90°, and greater than 90°.
2. How many degrees is the angle that is formed by clock hands at 6:00?
Read the Lesson3. Give three possible names for the angle shown to the right.
4. Draw the correct angle under each heading.
Obtuse angle Acute angle
Right angle Straight angle
5. Fill in the blanks with the correct angle number.
� and � are vertical angles.
� and � are adjacent angles.
Remember What You Learned6. Work with a partner. Have your partner draw two angles. Identify the
types of angles your partner has drawn.
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Study Guide and InterventionAngle Relationships
Chapter 10 10 Glencoe California Mathematics, Grade 6
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Classify each angle as acute, obtuse, right, or straight.
A. The angle is less B.than 90°, so it isan acute angle.
Label the two angles vertical or adjacent.
C. These angles are D.vertical because they are opposite each other and formed by two intersecting lines.
Classify each angle as acute, obtuse, right, or straight.
1. 2. 3. 4.
Label the angles vertical or adjacent.
5. 6. 7. 8.7
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• An angle has two sides that share a common endpoint. The point where the sides meet is called thevertex. Angles are measured in degrees, where 1 degree is one of 360 equal parts of a circle.
• Angles are classified according to their measure.
• Two angles are vertical if they are opposite angles formed by the intersection of two lines.
• Two angles are adjacent if they share a common vertex, a common side, and do not overlap.
Right Angle Acute Angle Obtuse Angle Straight Angle
Example 1
Example 2
Exercises
The angle is greaterthan 90°, so it is anobtuse angle.
These angles areadjacent because theyshare a common vertex,a common side, and donot overlap.
�1 and �3 are vertical angles.�4 and �2 are vertical angles.
�5 and �6 are adjacent angles
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Skills PracticeAngle Relationships
Chapter 10 11 Glencoe California Mathematics, Grade 6
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Classify each angle as acute, obtuse, right, or straight.
1. 2. 3.
4. 5. 6.
7. 8. 9.
Estimate the measurement of each angle in degrees.
10. 11. 12.
Use the figure at the right to answer Questions 13–15.
13. Name the acute angles.
14. Name the obtuse angles.
15. Name two angles that are adjacent.
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Name each angle in four ways. Then classify the angle as acute, right,obtuse, or straight.
1. 2. 3.
4. 5. 6.
Use the figure at the right to answer Questions 7 and 8.
7. Name two angles that are vertical.
8. Name two angles that are adjacent.
Use the figure at the right to name the following.
9. two acute angles
10. two straight angles
11. two right angles
12. two obtuse angles
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PracticeAngle Relationships
Chapter 10 12 Glencoe California Mathematics, Grade 6
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Word Problem PracticeAngle Relationships
Chapter 10 13 Glencoe California Mathematics, Grade 6
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1. CLOCKS The time shown on the clock is 11:05. Starting at this time,approximately what time will it bewhen the hands form an obtuse angle?
2. AIRPORT The runways at a local airport are sketched in the figure.Classify �1 and �2 as acute, obtuse,right, or straight.
21
3. FOUR SQUARE Lauren, James, Lisa,and Lauretta were playing four square.Which students are standing at vertical angles from one another?
Lauren James
Lisa Lauretta
4. CLOCKS The time shown on the clock is12:07. After 20 minutes have gone by,will the angle formed by the hour andminute hands be acute, obtuse, right,or straight?
5. BALLET When a ballet dancer’s feet arein first position, the heels are touching,and the feet are turned out. A dancerwith excellent technique can positionhis or her feet so that they are nearlyin a straight line. Isabella is practicingher technique. Classify the angle herfeet form as acute, obtuse, or right.
6. PARKING LOT Eric, Ryan, Aisha, and Abbey are all parked in the school lot.Who is parked at adjacent angles fromone another?
Aisha
RyanEric
Abbey
6MG2.1
Angles in BaseballAngles play an important part in many sports. In baseball, infieldersstand on and cover different parts of the infield depending on theposition of the runners. Sometimes, a player will have to turn varyingangles to make plays.
For Exercises 1 and 2, look at these pictures of baseball fields. In eachone, the four infielders cover different areas of the diamond. Use aprotractor to determine the measure of the angle of the area coveredby the 2nd baseman with different runner positions.
1. 2.
3. The outfield is covered by three other players:the left, center, and right outfielders. The areasthey cover may overlap slightly depending onwhoever is closest to the ball; but in general,each player has an area to cover. This figure shows the area most often covered by each outfielder. What type of angle does each area make with home plate? What type of angle do all three outfield areas combined create with home plate?
4. During a game, the pitcher notices the runner on second base wants to steal third base. If the pitcher is facing home plate, what type of angle does the pitcher have to turn through to throw the ball to third base?
5. During a different inning, a runner is on first base and appears to wantto steal second base. What type of angle does the pitcher need to turnthrough to throw the ball to second base if the pitcher is facing homeplate?
HomePlate
ThirdBase
SecondBase Area covered
by right fielder
Area coveredby center fielder
Area coveredby left fielder
FirstBase
HomePlate
ThirdBase
SecondBase Area covered by the
second baseman
FirstBase
HomePlate
ThirdBase
SecondBase Area covered by the
second baseman
FirstBase
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 10 14 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-1 6MG2.1
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 15 Glencoe California Mathematics, Grade 6
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Get Ready for the LessonComplete the Mini Lab at the top of page 514 in your textbook.Write your answers below.
1. Classify the angle as acute, right, obtuse, or straight.
2. Copy the angle onto a piece of paper. Then draw a ray that cuts the angle into two congruent angles. Label these two congruent angles �1 and �2.
3. What is m�1 and m�2?
4. What is the sum of m�1 and m�2?
5. Copy the original angle onto a piece of paper. Then draw a ray that separates the angle into two non-congruentangles. Label these two angles �3 and �4.
6. What is true about the sum of m�3 and m�4?
7. Complete Exercises 1–6 for the angle shown at the right.
Read the LessonFill in the blanks to answer Questions 8 and 9.
8. Two angles are complementary if the sum of their measure is .
9. Two angles are supplementary if the sum of their measure is .
Remember What You Learned10. 11.
45°x°35°
x°
6MG2.1, 6MG2.2Lesson Reading GuideComplementary and Supplementary Angles
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 16 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-2
Find the value of x.
The two angles form a right angle or 90°, so they are complementary,
Write the equation.Subtract 43 from each side.
so the value of x is 47°.
Find the value of x.
The two angles form a straight line or 180°, so they are supplementary,
Write the equation.Subtract 110 from each side.
so the value of x is 70°.
Find the value of x in each figure.
1. 2. 3.
4. 5. 6.
82° x°45°x°71°
x°
85°x°
56°
x°
58° x°
110 � x � 180� 110 � 110
x � 70110˚ x ˚
43 � x � 90� 43 � 43
x � 4743°
x°
• Two angles are complementary if the sum of their measure is 90°.
m�1 � m�2 � 90°
• Two angles are supplementary if the sum of their measure is 180°.
m�3 � m�4 � 180°
• To find a missing angle measure, first determine if the angles are complementary orsupplementary. Then write an equation and subtract to find the missing measure.
3 4
12
Example 1
Example 2
Exercises
6MG2.1, 6MG2.2Study Guide and InterventionComplementary and Supplementary Angles
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 17 Glencoe California Mathematics, Grade 6
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on
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10-2
Find the missing angle measure.
1. 2. 3.
4. 5. 6.
7. 8. 9.
Use the figure at the right to answer Questions 10–13.
10. Find m�HJL.
11. �HJL and �LJM are what type of angles?
12. Find m�KJM.
13. �KJL and �LJM are what type of angles?
K
JH M
L
90°30°
60°
24°
x°
43°
43° x°45° 65°
x°
10° x°
85° x°
42°
x°
25˚
x ˚42˚
x ˚127˚ x ˚
6MG2.1, 6MG2.2Skills PracticeComplementary and Supplementary Angles
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 18 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-2
Find the value of x in each figure.
1. 2. 3.
4. 5. 6.
Classify each pair of angles as complementary, supplementary, or neither.
7. 8. 9.
ALGEBRA Find the value of x in each figure.
10. 11. 12.
13. ALGEBRA If �C and �D are supplementary, and the measure of �Dis 45°, what is the measure of �C?
19.2˚ x˚
92˚ 78.5˚
x˚
49.1˚
x˚
12
12
1 2
72° x°110°
x°29°
x°
43°
x°65°x°22°
x°
6MG2.1, 6MG2.2PracticeComplementary and Supplementary Angles
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 19 Glencoe California Mathematics, Grade 6
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1. SIGN The support wire for a sign meets the wall and the overhang asshown below. If m�2 � 42°, find m�1.Explain your reasoning
21
2. STREETS Main Street intersects Oak Road. If a right-hand turn ontoOak Road requires a 77° turn, whatdegree must a left-hand turn onto Oak Road make?
77˚
Oak Road
Main Street
3. RAILROAD East of the town of Rockport,the railroad tracks intersect Highway 67as shown below. If m�1 � 133°, find m�2. Explain your reasoning.
12
4. CAMPING Jonna and Elizabeth found alevel campsite and pitched their tent asshown below. If m�1 � 120°, find m�2.Explain your reasoning.
2 1
5. GAS GAUGE Below is a picture of the gas gauge in Sergio's car. Theangles made by the indicator arecomplementary. If the m�1 � 42°,what is the m�2?
FUEL
E F1 2
6. ARCHITECTURE The plans for a newaquarium call for several hallways ofexhibits leading out of a circular mainroom. Because of the size of the tanksthat will be used, the angle formedbetween two adjacent hallways can beno smaller than 65°. What is themaximum number of hallways that canbe built leading out of the main room?
Main Room Hallway
Hallway
65˚
6MG2.1, 6MG2.2Word Problem PracticeComplementary and Supplementary Angles
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 10 20 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-2
Matchstick PuzzlesThe puzzles on this page involve a box of wooden matches.Toothpicks or any other straight objects may be also be used.
Use the square figure at the right to make each of the followingfigures.
1. Move 3 matches to make 2. Move 4 matches to make3 identical squares. 3 identical squares.
3. Remove 2 matches to 4. Move 2 matches to makemake 2 squares. 7 squares. (You may cross
the matches in this one only.)
Use the hexagonal figure at the right to make each of the following firgures.
5. Move 4 matches to make 6. Move 4 matches to make3 equilateral triangles. 4 identical diamonds.
Use the square figure at the right to make each of the following firgures.
5. Remove 4 matches to 6. Remove 6 matches to makemake 5 identical squares. 5 identical squares.
6MG2.3
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 21 Glencoe California Mathematics, Grade 6
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Get Ready for the LessonRead the introduction at the top of page 518 in your textbook.Write your answers below.
1. Explain how you know that each person surveyed chose only one shade ofblue.
2. If 500 people took part in the survey, how many preferred aquamarine?
Read the Lesson3. In the following circle graph, what is the percent represented by
section C? How do you know?
4. As stated in Example 2 on page 519, when you construct a circle graph,you can check your work by measuring the last section of a circle graph to verify that the angles have the correct measures. Why will this work as a check?
Remember What You Learned5. If you are given the results of a survey and the results are given in
percents, how do you draw a circle graph to represent the results of thesurvey? Describe each step.
Successful SpaceLaunches, 2001
12.5%B
C
25%A
5SDAP1.2Lesson Reading GuideStatistics: Display Data in a Circle Graph
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 22 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-3
Exercises
ENERGY Make a circlegraph of the data in thetable.
Step 1 Find the total number of reactors:104 � 59 � 54 � 222 � 439.
Step 2 Find the ratio that compares eachnumber with the total. Write theratio as a decimal rounded to the nearest hundredth.
United States: �140349�
� 0.24 Japan: �45349�
� 0.12
France: �45399�
� 0.13 Other: �242329�
� 0.51Step 3 Find the number of degrees for each section of the graph.
United States: 0.24 · 360� � 86� Japan: 0.12 · 360� � 43�
France: 0.13 · 360� � 47� Other: 0.51 · 360� � 184�
Step 4 Use a compass to construct a circle and draw a radius. Then use a protractor to draw an 86° angle. This represents the percent of nuclear reactors in the United States.
Step 5 From the new radius, draw a 47° angle forFrance. Repeat this step for the other twosections. Label each section and give the graph a title.
1. SWIMMING The table shows the number of members of the swim teamwho competed at the swim meet. Each competed in only one event. Makea circle graph of the data.
Nuclear Reactors in Operation, 2001
24%UnitedStates
51%Other
Countries
12%Japan
13%France
A graph that shows data as parts of a whole circle is called a circle graph. In a circle graph, the percents add up to 100. When percents are not given, you must first determine what part of the wholeeach item represents.
Swim Team Member Participation
Butterfly
Event Number
Freestyle 18
Breaststroke 7
Backstroke 5
2
Swim Team Member Participation
Example 1
Other Countries
United States 104
France 59
Japan 54
222
Country Number of Reactors
Nuclear Reactors in Operation, 2001
5SDAP1.2Study Guide and InterventionStatistics: Display Data in a Circle Graph
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 23 Glencoe California Mathematics, Grade 6
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For each table, find the number of degrees in each section of a circlegraph. Then make a circle graph of the data.
1. 2.
3. 4.
United States CoastlineSuccessful Space Launches, 2001
Family Members Students Confide InUnited States Energy Usage, 2001
United States Energy Usage, 2001
Other
Category Percent
Commercial and Industrial 52%
Residential 20%
Transportation 27%
1%
Family Members Students Confide In
Grandparent/Other
Family Member Percent
Mom 52%
Dad 17%
Brother/Sister 16%
15%
Successful Space Launches, 2001
China
Country Number
India 2
United States 23
European Space Agency 7
1
United States Coastline
Coast Length (miles)
Atlantic 2,100
Pacific 7,600
Gulf 1,600
Arctic 1,100
United States Coastline
Arctic
Coast Length (mi)
Atlantic 2,100
Pacific 7,600
Gulf 1,600
1,100
5SDAP1.2Skills PracticeStatistics: Display Data in a Circle Graph
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 24 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-3
Display each set of data in a circle graph.
1. 2.
EXPORTS For Exercises 3 and 4, use the circle graph that shows the percent of Persian Gulfpetroleum exports by country for the year2003.
3. Which country has the most petroleum exports?
4. How many times more exports does Iran have than Qatar?
DATA SENSE For each graph, find the missing values.
5. 6. Time Management
Chores28˚
Other36˚ Sleep
130˚
Meals42˚
Hygiene24˚
Schoolx˚
Recycled Products
Aluminum25% Electronics
x%
Plastic20%
Other15%
Newspaper30%
Persian Gulf Exports 2003
SaudiArabia49%
Iraq5% Iran
15%
Kuwait12%
Qatar5%
United ArabEmirates14%
America’s Energy SourcesVolume of World’s Oceans
America’s Energy SourcesType Percent
Petroleum 40%Natural Gas 23%
Coal 22%Nuclear 8%Other 7%
Volume of World’s OceansOcean PercentPacific 49%
Atlantic 26%Indian 21%Arctic 4%
Source: conocophillips.com
Source: peacecorps.gov
5SDAP1.2PracticeStatistics: Display Data in a Circle Graph
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 25 Glencoe California Mathematics, Grade 6
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LANGUAGES For Exercises 1 and 2,use the table that shows thenumber of people that speak thefive languages that are spokenby the most people in the world.
MILITARY For Exercises 3 and 4, use the table that shows the numberof people active in the United Statesmilitary in 2002.
CategoryCommercial and IndustrialResidentialTransportationOther
Spanish
Language Speakers (millions)
Hindi 366
English 341
322
Bengali 207
Chinese, Mandarin 874
Languages Spoken by the Most People
1. Find the degrees for each part of acircle graph that shows the data.
2. Make a circle graph of the data. Whichthree languages account for 41% of thetotal?
Languages Spoken by the Most People
Coast Guard
Air Force
Branch Personnel (thousands)
Navy 385
Marine Corps 174
368
38
Army 486
3. Make a circle graph of the data.United States Military Personnel Active Duty, 2002
4. Which two branches taken togetheraccount for almost half of the total?
United States Military, Active Duty, 2002
5SDAP1.2Word Problem PracticeStatistics: Display Data in a Circle Graph
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 26 Glencoe California Mathematics, Grade 6
10-3 Enrichment
Relative Frequency and Circle GraphsThe relative frequency tells how the frequencyof one item compares to the total of all thefrequencies. Relative frequencies are written asfractions, decimals, or percents.
For example, in Exercise 1 below, the total of allthe frequencies is 50. So, the relative frequency ofthe grade A is 8 � 50, or 0.16.
The circle at the right is divided into 20 equalparts. You can trace this circle and then userelative frequencies to make circle graphs.
Complete each chart to show the relativefrequencies. Then sketch a circle graph forthe data. Use decimals rounded to the nearest hundredth.
1. History Grades for 50 Students
2. Steve’s Budget
D 6
C18Frequency
8
16
Grade
18
A
6
B
RelativeFrequency
C
D
0.16
2F
AmountSpent
$26
$46
Item
$24
Telephone
$38
Movies
RelativeSpending
Books
Car
$66Other
0 0.050.1
0.15
0.2
0.3
0.35
0.40.450.50.55
0.25
0.6
0.65
0.7
0.75
0.8
0.85
0.90.95
History Grades for 50 Students
Steve’s Budget
5SDAP1.2
NAME ________________________________________ DATE ______________ PERIOD _____
TI-73 ActivityCircle Graphs
Chapter 10 27 Glencoe California Mathematics, Grade 6
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Use your calculator to make circle graphs from data.
A group of students took a survey of favorite soft drinks. Make a circle graph
and find the percent of each favorite soft drink. Here is theirdata table.
Step 1 Enter the data into lists. Enter the category data in L1and the number data in L2. Remember to use quotesaround the first item in the category data. You canabbreviate the category names.
[MEM] 6 Move right and highlight the first blank list.Name the category DRINK.
[TEXT] " D R I N K " Done
[TEXT] " C O L A " Done
Note: The letter c appears in L1, because it contains category data.Fill in the rest of the drink categories. Enter the number data in a list called NUMBER.
Step 2 Set Plot 1. First turn off all plots.
[PLOT] 4
[PLOT] 1
Make sure Drink is the CategList and Number is the Data List. Choose Number.
Step 3 Create the circle graph. Analyze the graph.
Use cursor keys with .
Step 4 Create a circle graph showing percents. Choose Percent on the Plot 1 screen.
[PLOT] 1
In the key shown beside the graph, read the percents for each soft drink.
Refer to circle graph you created.
1. Describe the circle graph.
2. Use the percent circle graph. List the percents for each soft drink.
3. What does the circle graph tell you about the favorite soft drinks of the studentssurveyed? Use percents in your description.
GRAPHENTER2nd
TRACEGRAPH
TRACE
ENTER
ENTERENTER2nd
ENTER2nd
ENTER2nd
ENTER2nd
LISTENTER2nd
Category Number of(Soft Drink) Students
cola 28
diet cola (DC) 9
root beer (RB) 26
lemon-lime (LL) 13
other 8
Example
Exercises
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson Reading Guide Triangles
Chapter 10 28 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-4
Get Ready for the LessonComplete the Mini Lab at the top of page 524 in your textbook. Writeyour answers below.
1. What kind of angle is formed where the three vertices meet?
2. Repeat the activity with another triangle. Make a conjecture about thesum of the measures of the angles of any triangle.
Read the Lesson3. How can you indicate that two sides of a triangle are congruent?
4. Write the following equation in words: m�1 � m�2 � m�3 � 180�.
5. If you know the measures of two angles of a triangle, how can you findthe measure of the third angle?
Remember What You Learned6. Complete the table to help you remember the ways to classify triangles.
Classified by Angles or Sides
angles
Type of Triangle
sides
acute
obtuse
Description
no congruent sides
1 right angle
isosceles
equilateral
6MG2.2, 6MG2.3
Exercises
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionTriangles
Chapter 10 29 Glencoe California Mathematics, Grade 6
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Find the value of x in �ABC.
x � 66 � 52 � 180 The sum of the measures is 180.x � 118 � 180 Simplify.
� 118 � 118 Subtract 118 from each side.x � 62
The missing angle is 62�.
Classify the triangle by its angles and by its sides.
The triangle has one obtuse angle and two sides the same length. So, it is an obtuse, isosceles triangle.
Find the missing measure in each triangle. Then classify the triangleas acute, right, or obtuse.
1. 2. 3.
Classify each triangle by its angles and by its sides.
4. 5. 6.
40˚
110˚ 30˚
60˚
70˚50˚
45˚
40˚ x˚43˚
x˚82˚
˚x75˚
Triangles can be classified by the measures of their angles. An acute triangle has three acute angles.An obtuse triangle has one obtuse angle. A right triangle has one right angle.
Triangles can also be classified by the lengths of their sides. Sides that are the same length arecongruent segments and are often marked by tick marks. In a scalene triangle, all sides havedifferent lengths. An isosceles triangle has at least two congruent sides. An equilateral triangle hasall three sides congruent.
A triangle is a figure with three sides and three angles. The symbol for triangle is �. The sum of the measures of the angles of a triangle is 180�.You can use this to find a missing angle measure in a triangle.
A
B
C
66˚
˚x52˚
120˚
Example 1
Example 2
6MG2.2, 6MG2.3
NAME ________________________________________ DATE ______________ PERIOD _____
Skills PracticeTriangles
Chapter 10 30 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-4
Find the missing measure in each triangle. Then classify the triangleas acute, right, or obtuse.
1. 2. 3.
4. 5. 6.
7. 8. 9.
Classify each triangle by its angles and by its sides.
10. 11. 12.
13. 14. 15.
16. 17. 18.
27˚46˚
82˚
52˚
98˚
121˚40˚
19˚60˚
60˚
60˚
50˚
40˚114˚
37˚
50˚x˚
126˚ 22˚
x˚51˚
57˚
x˚
71˚
45˚x˚
65˚
x˚38˚
38˚
x˚
49˚
x˚24˚
36˚
x˚
81˚84˚x˚
6MG2.2, 6MG2.3
Find the value of x.
1. 2. 3.
4. 5. 6.
Find the missing measure in each triangle with the given angle measures.
7. 45°, 35.8°, x° 8. 100°, x°, 40.7° 9. x°, 90°, 16.5°
10. Find the third angle of a right triangle if one of the angles measures 24°.
11. What is the third angle of a right triangle if one of the angles measures 51.1°?
12. ALGEBRA Find m�A in � ABC if m�B � 38° and m�C � 38°.
13. ALGEBRA In �XYZ, m�Z � 113° and m�X � 28°. What is m�Y?
Classify the marked triangle in each object by its angles and by its sides.
14. 15. 16.
ALGEBRA Find the value of x in each triangle.
20. 21. 22.
2x˚ x˚
x˚7x˚
3x˚
2x˚ 2x˚
x˚
30˚ 30˚40˚
50˚25˚
60˚
60˚̊
x˚
41˚
37˚x˚
29˚
61˚̊
x˚
17˚
x˚
22˚
140˚ x˚
42˚ x˚
NAME ________________________________________ DATE ______________ PERIOD _____
PracticeTriangles
Chapter 10 31 Glencoe California Mathematics, Grade 6
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NAME ________________________________________ DATE ______________ PERIOD _____
Word Problem PracticeTriangles
Chapter 10 32 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-4
1. TAILORING Each lapel on a suit jacket isin the shape of a triangle. The threeangles of each triangle measure 47�,68�, and 65�. Classify the triangle by itsangles.
2. FLAGS A naval distress signal flag is inthe shape of a triangle. The three sidesof the triangle measure 5 feet, 9 feet,and 9 feet. Classify the triangle by itssides.
3. CARPENTRY The supports of a woodtable are in the shape of a righttriangle. Find the third angle of thetriangle if the measure of one of theangles is 23�.
4. MAPS The three towns of Ripon,Sparta, and Walker form a triangle asshown below. Classify the triangle byits angles and by its sides. What is thevalue of x in the triangle?
38˚
104˚ ˚x
Ripon
Sparta Walker
47 mi30 mi
30 mi
5. HIKING The figure shows the OakCreek trail, which is shaped like atriangle. Classify the triangle by itsangles and by its sides. What is thevalue of x in the figure?
61˚
78˚ ˚x
Rocky Peak
Meadow Trail Head
1.2 mi0.8 mi
1.1 mi
Oak Creek
6. LADDER The figure shows a ladderleaning against a wall, forming atriangle. Classify the triangle by itsangles and by its sides. What is thevalue of x in the figure?
66˚
˚x
9 ft
4 ft
6MG2.2, 6MG2.3
Triangle SumsThe measures of the angles of a triangle always add up to 180°. Thesides of a triangle also have a special relationship. In this activity,you will explore the relationships of the side lengths.Cut the strips of paper from the right side of this page. Use the 3specified strips for each problem. Tell if a triangle can be formedwith them. If so, tell what type of triangle it is.
1. 6 cm, 14 cm, and 14 cm 2. 6 cm, 6 cm, 14 cm
3. 6 cm, 8 cm, 14 cm 4. 3 cm, 3 cm, 6 cm
5. 3 cm, 6 cm, 8 cm 6. 6 cm, 6 cm, 8 cm
7. Look at your answers above. Choose any set of side lengths that form atriangle. Add the two shortest measures. Compare that sum with thelongest side length. Try this with all the triangles above. What conclusioncan you make about triangle side lengths?
8. Now look at the sets of side lengths that did not form triangles. Add thetwo shortest sides. Compare the sum with the length of the third side.What conclusion can you make about three lengths that do not make atriangle?
9. What rule can you give to test any three segment lengths to find out ifthe segments will form a triangle?
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 10 33 Glencoe California Mathematics, Grade 6
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Example Use the formula d � rt where d is distance, r is rate, and t is time to determine how far a car has traveled after 4 hours if
it is traveling at a rate of 65 mph.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 34 Glencoe California Mathematics, Grade 6
Copyright ©
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cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-5
Logical reasoning is a method of problem solving that uses inductive reasoning, making a rule afterseeing several examples or deducting reasoning, use a rule to make a decision.
Explore You know the car has traveled for 4 hours at 65 mph.Plan Try a few examples to find a pattern. Make a table.
Solve
After each hour the car has traveled 65 more miles. So after 4 hours the carwill have traveled 260 miles.
Examine The formula is d � rt so d � 65 � 4 or 260 mi.
Hours Passed Distance Traveled(in miles)
1 651.5 97.52 130
2.5 162.53 195t 65t
Solve the following problems using logical reasoning.
1. TRAVEL Use the formula d � rt where d is the distance, r is the rate, andt is the time to determine how far the Moralez family has traveled if theyare driving at a rate of 72 miles per hour for 9 hours.
2. CELL PHONES Determine the cost per phone call if Maria made 30 callslast month and her total bill for the month was $45.00.
3. MUSIC Sarah, Juan, and Derrick play the piano, trumpet, and violin, butnot necessarily in that order. Sarah and Derrick sit on either side of thetrumpet player. Sarah does not play the violin. Who plays the violin?
Exercises
6MR1.2, 6MG2.3Study Guide and InterventionProblem-Solving Investigation: Use Logical Reasoning
Use logical reasoning to solve.
1. GEOMETRY Draw several squares and measure their interior angles. Whatcan you conclude about the measures of the angles of a square? Did youuse inductive or deductive reasoning?
2. MONEY Luke is investing money in a savings account. Use the formula I � Prt where I is the amount of interest earned, P is the principalamount of money invested, r is the interest rate, and t is the length oftime the money is invested. If Luke invests 500 at 5% interest for 1 year,how much interest will he earn? Did you use inductive or deductivereasoning?
3. PATTERNS Write a rule to represent the pattern shown below. Did you useinductive or deductive reasoning? 2, 4, 6, 8, 10, …
4. STUDENT COUNCIL Chen, Sue and Jacob are president, vice president andsecretary of the student council, not necessarily in that order. Chen andthe vice president stayed after school with Jacob to plan a dance. Chen isnot the president. Who is the president?
5. GEOMETRY Draw several parallelograms and measure their sides. Whatcan you conclude about the measures of the opposite sides of aparallelogram? Did you use inductive or deductive reasoning?
6. TRAVEL Use the formula D � rt where D is the distance, r is the rate, andt is the time to determine how far Lucinda traveled if she drove 65 milesper hour for 6 hours without stopping. Did you use inductive or deductivereasoning?
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 35 Glencoe California Mathematics, Grade 6
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Problem-Solving Investigation: Use Logical Reasoning
Select the Operation
Mixed Problem Solving
For Exercises 1 and 2, use logicalreasoning to solve the problem.
1. TOWNS Tia, Bianca, and Hiroko live inthe towns of Parkside, Westlake, andSummerville, but not necessarily in thatorder. Tia and her friend that lives inWestlake helped Bianca with her chores.Bianca does not live in Parkside. Wheredoes Tia live? Did you use inductive ordeductive reasoning?
2. GEOMETRY Draw a right triangle. Markthe midpoints of each side of thetriangle and draw a smaller triangle byconnecting the midpoints. Do thisseveral more times. What can youconclude about the smaller triangle? Did you use inductive or deductivereasoning?
Use any strategy to solve Exercises 3and 4. Some strategies are shown below.
3. ANGLES One angle of a triangle is 33°less than the other two angles. Find themeasures of the angles of the triangle.Did you use inductive or deductivereasoning?
4. METEORITES An astronomer found threemeteorites weighing 9.4 pounds, 5.7pounds, and 24.5 pounds. If 1 kilogramweighs 2.2 pounds, find the averagemass of the meteorites in kilograms.
For Exercises 5 and 6, select theappropriate operation(s) to solve theproblems. Justify your selections andsolve the problem.
5. PUBLIC TRANSPORTATION A bus stoppedat a bus stop and 12 people got on and 5 got off. At the next stop, 14 people goton and 3 got off. If the number ofpassengers has doubled, find thenumber of passengers on the bus.
6. DISCOUNTS The table shows thedifferent discounts two stores offer forthe same product. Which store offers thebetter price after the discount is appliedand by how much?
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 36 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-5
PROBLEM-SOLVING STRATEGIES
• Use the four-step plan.
• Look for a pattern.
• Use a graph.
• Use logical reasoning.
Price DiscountStore A $129.00 $25Store B $139.00 25%
6MR1.2, 6MG2.3PracticeProblem-Solving Investigation: Use Logical Reasoning
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 37 Glencoe California Mathematics, Grade 6
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1. PHYSICS A ball is dropped from a heightof 40 feet. If the ball bounces �
12
� as highon each successive bounce, what is theheight on the fourth bounce?
2. RECIPES Shawn is making a cake. Heneeds a total of 3�
14
� cups of flour. If hehas already added 2�
12
� cups, how muchmore does he need to add?A 2 cups C �
12
� cup
B 1 cup D �34
� cup
3. GEOMETRY Draw several pentagonsand measure their interior angles.What can you conclude about the sumof the measures of the angles of apentagon? Did you use inductive ordeductive reasoning?
4. PATTERNS Find the next three terms is the sequence.2, 5, 9, 14, …
5. WORK The table below shows howmuch Lu got paid based on the numberof hours she babysat. Predict her payfor 7 hours.
6. GEOMETRY Use the formula V � Bhwhere V is the volume of a cylinder,B is the area of the base and h is theheight of the cylinder to find thevolume of the cylinder below.
B = 3.5 in2
h = 8 in
7. FRAMING A photograph is 8 in. by 10 in. and is to be surrounded by a matthat is 1.5 in. all around. What will bethe dimensions of the picture and mattogether?
8. SCHOOL Students filled out a surveyabout their favorite school subjects. Theresults are shown in the bar graphbelow. How many more students listedEnglish as their favorite subject thanmath?
SocialStudies
Math English Science
20
10
0
3025
15
5
Number of hours Pay1 $52 $103 $154 $20
6MR1.2, 6MG2.3Word Problem PracticeProblem-Solving Investigation: Use Logical Reasoning
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson Reading Guide Quadrilaterals
Chapter 10 38 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
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panies, Inc.
10-6
Get Ready for the LessonRead the introduction at the top of page 533 in your textbook.Write your answers below.
1. Describe the angles inside the four-sided figure.
2. Which sides of the figure appear to be parallel?
3. Which sides appear to be congruent?
Read the Lesson4. In the diagram of quadrilaterals on page 533, what do the arrowheads on
the parallelogram and trapezoid indicate?
5. Why are all the figures on the page called quadrilaterals?
6. How is a trapezoid different from a rhombus, a square, and a rectangle?
7. In the diagrams of the parallelogram, rhombus, square, and rectangle,how do you know that certain sides are congruent?
Remember What You Learned8. Work with a partner. Take turns drawing quadrilaterals. Have the other
person give all possible names for the quadrilateral. Then decide on thebest name for the quadrilateral. For example, if one person draws asquare, the other person should say that it is a quadrilateral, aparallelogram, a rectangle, and a rhombus, but the best name for thefigure is a square.
6MG2.3
Example
Exercises
Quadrilaterals can be classified using their angles and sides. The best description of a quadrilateral isthe one that is the most specific.
Examples
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionQuadrilaterals
Chapter 10 39 Glencoe California Mathematics, Grade 6
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Classify the quadrilateral using the name that best describes it.
a The quadrilateral is a parallelogram with 4 congruent sides. It is a rhombus.
b The quadrilateral has one pair of parallel sides.It is a trapezoid.
c The quadrilateral is a parallelogram with 4 right angles.It is a rectangle.
Find the missing measure in the quadrilateral.
100 � 110 � 60 � x � 360 Write the equation.270 � x � 360 Simplify.
� 270 � 270 Subtract 270 from x � 90 each side.
So, the missing measure is 90°.
Classify the quadrilateral using the name that best describes it.
1. 2. 3.
Find the missing angle measure in each quadrilateral.
4. 5. 6.
125˚
54˚
96˚x˚95˚
72˚
82˚
x˚135˚
88˚45˚
x˚
100˚
110˚
60˚
x˚
Rectangle
parallelogram with4 right angles
Trapezoid
one pair of parallelsides
Rhombus
parallelogram with4 congruent sides
Square
parallelogram with4 right angles and4 congruent sides
Parallelogram
opposite sides parallel and
opposite sides congruent
6MG2.3
NAME ________________________________________ DATE ______________ PERIOD _____
Skills PracticeQuadrilaterals
Chapter 10 40 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-6
Classify the quadrilateral using the name that best describes it.
1. 2. 3.
4. 5. 6.
7. 8. 9.
Find the missing angle measure of each quadrilateral.
10. 11. 12.
13. 14. 15.
64˚
x˚
77˚
99˚ 109˚
x˚
72˚
121˚
x˚
89˚
92˚ 64˚
x˚135˚110˚
75˚x˚
52˚
x˚
6MG2.3
Classify each quadrilateral using the name that best describes it.
1. 2. 3.
4. 5. 6.
ALGEBRA Find the missing angle measure in each quadrilateral.
7. 8. 9.
10. 11. 12.
Find the missing measure in each quadrilateral with the given anglemeasures.
13. 63.2°, 56°, 111.7°, x° 14. 31.7°, x°, 161.3°, 51.4°
15. x°, 122.4°, 53.7°, 90° 16. 83.7°, 137.2°, x°, 28.5°
17. ALGEBRA Find m�C in quadrilateral ABCD if m�A � 110°, m�B � 88°,and m�D � 55°.
18. ALGEBRA What is m�Z in quadrilateral WXYZ if m�W � 86°, m�X � 88°,and m�Y � 92°?
ALGEBRA Find the value of x in each quadrilateral.
19. 20. 21.3x˚ 3x˚
3x˚ 3x˚
60˚
60˚ x˚
x˚68˚ 65˚
x˚ x˚
152˚
x˚120˚
110˚60˚
x˚
125˚
x˚
130˚ 50˚̊
50˚̊ x˚126˚78˚̊
54˚̊
x˚
107˚96˚̊
80˚̊
x˚
NAME ________________________________________ DATE ______________ PERIOD _____
PracticeQuadrilaterals
Chapter 10 41 Glencoe California Mathematics, Grade 6
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NAME ________________________________________ DATE ______________ PERIOD _____
Word Problem PracticeQuadrilaterals
Chapter 10 42 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-6
1. KITES A kite is shown below. What isthe best name to classify the shape ofthe kite? Explain.
2. MAPS A map showing the roadconnecting the towns of Pike, Hudson,Placid, and Alton is shown. The roadconnecting Pike and Hudson is parallelto the road connecting Alton andPlacid. What is the best name toclassify the shape of the roadsconnecting the four towns? Explain.
HudsonPike
PlacidAlton
N
3. ART A picture frame is shown below.What is the best name to classify theshape of the frame?
1 ft
1 ft
4. SCHOOL SUPPLIES The side view of aneraser is shown below. What is the bestname to classify the shape of theeraser?
5. PARTY The front of a birthday partyinvitation is shown below. Find themeasure of the missing angle.
60˚ 120˚
120˚ x˚PARTY!
6. TABLE The top of Mr. Bautista’s newcoffee table is shown below. Find themeasure of the missing angle.
60˚
120˚ 100˚
x˚
6MG2.3
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 10 43 Glencoe California Mathematics, Grade 6
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The Colormatch SquareTo work this puzzle, cut out the 16 tiles at the bottom of this page. The goal ofthe puzzle is to create a square so that the sides of any pair of adjacent tilesmatch. You are not allowed to rotate any of the tiles.
1. Complete the solution to the colormatch square puzzle below.
2. Find at least one other solution in which the A tile is in the upper leftcorner.
A D
PN
B G
L O
H
M
C
I KJ
FE
A
D
Whitesquaresmatch.
P
N
B
L
O
M
I
K
J
E
6MG2.3
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson Reading Guide Similar Figures
Chapter 10 44 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-7
Get Ready for the LessonComplete the Mini Lab in your textbook. Write your answers below.
1. A�B� on the smaller rectangle matches E�F� on the larger rectangle.Name all pairs of matching sides in each pair of figures.
2. Write each ratio in simplest form.
a. �AE
BF�; �
FB
GC�; �
HD
GC�; �
EA
HD� b. �
RXY
S�; �
SY
TZ�; �
RXZ
T�
3. What do you notice about the ratios of matching sides.
4. Name all pairs of matching angles in the figures above. What do younotice about the measure of these angles?
5. MAKE A CONJECTURE about figures that have the same shape but not necessarily the same size.
Read the Lesson6. Write the statement �ABC � �DEF in words.
7. Write the statement �A � �D in words.
8. Suppose you know that two figures are similar, and that the followingcorresponding sides are proportional: side JK corresponds to side DE, andside KL corresponds to side EF. How would you write a proportion to findthe length of side KL if the lengths of all other sides are known?
Remember What You Learned9. Think of a real-life example that you could measure using indirect
measurement if you were given a miniature replica of your example.Explain how you could find an unknown measurement using known measurements of your example and the measurements of the replica.
6NS1.3
Exercises
Example 1
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionSimilar Figures
Chapter 10 45 Glencoe California Mathematics, Grade 6
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If MNOP � RSTU, find the length of S�T�.
Since the two figures are similar, the ratios of their correspondingsides are equal. You can write and solve a proportion to find S�T�.
�UPO
T�� �
NST
O� Write a proportion.
�278�
� �n5
� Let n represent the length of ST. Then substitute.
7n � 28(5) Find the cross products.
7n � 140 Simplify.
n � 20 Divide each side by 7.
The length of S�T� is 20 feet.
Find the value of x in each pair of similar figures.
1. 2.
3. 4.
6 in.
5 in.
18 in.
B C
DA
F G
HE
x
9 yd
5 yd10 yd M N
OP
R S
TU
x
2 ft
4 ft
I
G
K
H
L
J
x
12 ft
3 m
5 m
A
B
F
C
D
E x
9 m
Figures that have the same shape but not necessarily the same size are similar figures. The symbol � means is similar to. You can use proportions to find the missing length of a side in a pair of similar figures.
For example �ABC � �DEF.Corresponding angles Corresponding sides
� A � � D �150� � �
48
� � �36
�
� B � � E
� C � � F
7 ft
5 ft
28 ft
M N
OP
R S
TU
4
3A
B
FC D
E
810
6
5
6NS1.3
NAME ________________________________________ DATE ______________ PERIOD _____
Skills PracticeSimilar Figures
Chapter 10 46 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-7
Find the value of x in each pair of similar figures.
1. 2.
3. 4.
5. 6.
Determine whether each pair of figures is similar. Justify youranswer.
7. 8.
24 m
40 m15 m
8 m
D
F
EA
C
B
7 cm
9 cm
14 cm
18 cm
15 in.
12 in.
20 in.
B C
DA
E F
GH
x
6 mm
4 mm
M
OQ N
P
R x
9 mm
10 cm
7 cm
21 cm
B C
DA
F G
HEx
12 ft
14 ftA
B
E
C F G
x
18 ft
H
D
7 m3 m
N
M
R
O
Q
P
x9 m4 ft
3 ft
A
B
F
C
D
E x
6 ft
6NS1.3
1. Which rectangle is similar to rectangle RSTU?
2. Which triangle is similar to triangle XYZ?
Find the value of x in each pair of similar figures.
3. 4.
5. 6.
7. FLAGPOLES Tasha wants to find the height ofthe flagpole at school. One morning, shedetermines the flagpole casts a shadow of 12 feet. If Tasha is 5 feet tall and casts a shadow of 3 feet, what is the height of theflagpole?
12 ft
x ft
3 ft
5 ft
4.2 mm1.5 mm
12.6 mm
x mm15 in.
8 in.24 in.
x in.
2 ft5 ft
7 ft
x ft 6 cm12 cm
12 cm
x cm
X
YZ
30 24 PR
T10 14
C
F
HGB
A32 3526 28
R S
TU
3
5
A B
CD
5
5
E FM N
Q PGH
6 8
10 2
NAME ________________________________________ DATE ______________ PERIOD _____
PracticeSimilar Figures
Chapter 10 47 Glencoe California Mathematics, Grade 6
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NAME ________________________________________ DATE ______________ PERIOD _____
Word Problem PracticeSimilar Figures
Chapter 10 48 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-7
MODEL CARS For Exercises 1 and 2, use the following information. A scale model racing car is 11 inches long,3 inches wide, and 2 inches tall. The actual racing car is shown at the right.
PHOTOGRAPHY For Exercises 3–4, use the given information. James wants to enlarge a photograph that is 6 inches wide and 4 inches tall so that it fits into the frame shown.
30 in.
22 ft
1. How wide is the actual racing car? 2. How tall is the actual racing car?
3. How tall must the frame be for thepicture to fit?
4. Suppose James cuts 1 inch from the width of the photo, so that it is 5 inches wide, before he makes theenlargement. How tall will the framehave to be for the picture to fit?
5. MAPS A map below shows the towns ofDover, Butler, and Lodi. If the actualdistance between Dover and Butler is24 miles, how far is it from Dover toLodi?
Lodi
ButlerDover
4 in.
3 in.
6. BLUEPRINTS A blueprint for a house isshown below. If the front of the houseis actually 30 feet wide, how tall is thehouse?
12 in.
14 in.
6NS1.3
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 10 49 Glencoe California Mathematics, Grade 6
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Similar Figures and AreasThe areas of two similar figures are related in a special way. Suppose that rectangle A is 2 units by3 units and rectangle B is 4 units by 6 units.
The area of rectangle A is 2 � 3 � 6 units2.
The area of rectangle B is 4 � 6 � 24 units2.
The lengths of the sides of rectangle B are twice those of rectangle A and the area of rectangle B is four times that of rectangle A.
Sketch figure B similar to figure A and satisfying the given condition.
1. Rectangle B has sixteen times the area of rectangle A.
2. Square B has an area that is 4 times that of square A.
3. Circle B has an area four times that of circle A.
Circle BCircle A
1.5
Square BSquare A
2
2
Rectangle BRectangle A
31
Rectangle BRectangle A
36
42
6NS1.3
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson Reading GuidePolygons and Tessellations
Chapter 10 50 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-8
Get Ready for the LessonRead the introduction at the top of page 546 in your textbook. Writeyour answers below.
1. Find the difference between the shapes of the states in Group 1 and theshapes of the states in Group 2.
2. Why do most states have boundaries that are not straight line segments?
Read the Lesson3. How many straight lines can a polygon have?
4. What is a simple figure?
5. When you draw a figure, how can you tell whether or not it is closed?
6. How do you find the sum of the angle measures in a regular polygon?
7. In this lesson, the terms vertex and vertices are used. How are the termsrelated?
Remember What You Learned8. Using dot paper, draw a tessellation different from the ones shown in this
lesson. You can use all the same shape or you can use combinations ofshapes that form patterns. Share your work with your class.
6MR2.2 , 6AF3.2
Examples
Exercises
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionPolygons and Tessellations
Chapter 10 51 Glencoe California Mathematics, Grade 6
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Determine whether each figure is a polygon. If it is, classify thepolygon and state whether it is regular. If it is not a polygon,explain why.
The figure has 5 congruent sides The figure is not a polygonand 5 congruent angles. It is a because it has sides that overlap.regular pentagon.
Determine whether each figure is a polygon. If it is, classify thepolygon and state whether it is regular. If it is not a polygon, explainwhy.
1. 2. 3.
4. 5. 6.
120˚
A polygon is a simple, closed figure formed by three or more straight lines. A simple figure does nothave lines that cross each other. You have drawn a closed figure when your pencil ends up where itstarted. Polygons can be classified by the number of sides they have.
A polygon that has all sides congruent and all angles congruent is called a regular polygon.
decagon10 sides
nonagon9 sides
octagon8 sides
heptagon7 sides
hexagon6 sides
pentagon5 sides
6MR2.2 , 6AF3.2
NAME ________________________________________ DATE ______________ PERIOD _____
Skills PracticePolygons and Tessellations
Chapter 10 52 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
10-8
Determine whether each figure is a polygon. If it is, classify the polygonand state whether it is regular. If it is not a polygon, explain why.
1. 2. 3.
4. 5. 6.
7. 8. 9.
Find the measure of an angle in each polygon.
10. regular 15-gon 11. regular 18-gon 12. regular 24-gon
Classify the polygons that are used to create each tessellation.
13. 14.
15. What is the perimeter of a regular pentagon with sides 8.4 inches long?
6MR2.2 , 6AF3.2
Determine whether each figure is a polygon. If it is, classify the polygonand state whether it is regular. If it is not a polygon, explain why.
1. 2. 3.
4. 5. 6.
Find the measure of an angle in each polygon if the polygon is regular. Round tothe nearest tenth of a degree if necessary.
7. dodecagon 8. 14-gon 9. 18-gon 10. 36-gon(12-sided)
Classify the polygons that are used to create each tessellation.
11. 12.
13. What is the perimeter of a regular decagon with sides 6.2 meters long?
14. Find the perimeter of a regular hexagon having sides 5�23
� inches long.
KITES For Exercises 15–17, use the following information. A kite manufacturer makes kites in the shape of the figure shown.
15. Classify the shape of the kite.
16. If �K � �T and �E � 30°, find m�K and m�T.
17. Can a tessellation be made by using the shape of the kite? Justify your answer.
K T
I
E
NAME ________________________________________ DATE ______________ PERIOD _____
PracticePolygons and Tessellations
Chapter 10 53 Glencoe California Mathematics, Grade 6
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Word Problem PracticePolygons and Tessellations
Chapter 10 54 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
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-Hill, a division of T
he McG
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panies, Inc.
10-8
1. ROYALTY The outline of a crown wornby a king is shown below. Is the figurea polygon? If it is, classify the polygonand state whether it is regular. If it isnot a polygon, explain why.
2. ALCHEMY The symbol shown is one of the signs for salt alkali used in 17th-century chemistry. Is the symbol a polygon? If it is, classify the polygonand state whether it is regular. If it isnot a polygon, explain why.
3. JEWELRY The symbol shown is oftenused to represent gems. Is the symbol apolygon? If it is, classify the polygonand state whether it is regular. If it isnot a polygon, explain why.
4. SYMBOLS The 5-pointed star shown hassides of equal length. Is the symbol apolygon? If it is, classify the polygonand state whether it is regular. If it isnot a polygon, explain why.
5. STAIRS The figure shows a side view ofa set of stairs. Is the figure a polygon?If it is, classify the polygon and statewhether it is regular. If it is not apolygon, explain why.
6. TESSELLATIONS Identify the polygonsthat are used to create the tessellationshown in the figure.
6MR2.2 , 6AF3.2
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 10 55 Glencoe California Mathematics, Grade 6
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Tessellated Patterns for Solid ShapesTessellations made from equilateral triangles can be used to buildthree-dimensional shapes. In Exercise 1, you should get a shape likethe one shown at the right. It is called a pyramid.
Copy each pattern. Crease the pattern along the lines.Then follow directions for folding the pattern. Use tape to secure the folded parts. When you have finished each model,describe it in words.
1. Fold 5 over 1.Repeat, in this order:
fold 6 over 7,fold 2 over 6.
2. Cut between 4 and 5. Then fold 5 over 3.Repeat in this order:
fold 6 over 5,fold 7 over 12, andfold 2 over 9.
3. Cut between 1 and 2 and between 14 and 15. Then fold 15 over 14.Repeat, in this order:
fold 1 over 2,fold 4 over 3,fold 11 over 1,fold 16 over 5, andfold 12 over 13.
1
5 710
14
69 11
12 13 15
16
2
8
3 4
3
8 107 9
12
2
4
11
5 6
1
1
3 52 4
7
6
6MR2.2 , 6AF3.2
NAME ________________________________________ DATE ______________ PERIOD _____
TI-73 ActivityInterior Angles
Chapter 10 56 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
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-Hill, a division of T
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panies, Inc.
10-8
Use your calculator to explore interior angles of polygons. The sum of the measures of theinterior angles of a polygon with n sides is: Sum � (n � 2) � 180°.
If the polygon is regular, then the measure of each interior is this Sum divided by n, or �Sunm�.
Use and these formulas to complete the table below.
Step 1 Clear all lists. [MEM] 6
Step 2 Open the List feature.
Step 3 In L1, enter n, the number of sides.
Press after each value.
Step 4 In L2, enter the Sum of Interior Angles formula.
Highlight L2.
[TEXT] " Done [STAT] 1 2 180
[TEXT] " Done
Step 5 Highlight L3 and enter the formula for the measure of each angle.
[TEXT] " Done [STAT] 2 [STAT] 1
[TEXT] " Done 1. Check that the angle
measures for the octagon are correct by evaluating the expressions when n � 8.Do your calculations match the list values?
2. Describe the trends you see in the sum and the angle measure columns.
ENTERENTER
2nd2nd2nd2nd
ENTERENTER2nd
)2nd(2nd
ENTER
LIST
ENTER2nd
LIST
Name of Polygon Each Angle(Regular Polygon)
3 triangle 180° 60°
4
5
6
7
8
9
10
No. of Sides
Sum of InteriorAngles
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson Reading GuideTranslations
Chapter 10 57 Glencoe California Mathematics, Grade 6
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Get Ready for the LessonComplete the Mini Lab at the top of page 553 in your textbook. Writeyour answers below.
1. Trace the horizontal and vertical path between corresponding vertices.What do you notice?
2. Add 5 to each x-coordinate of the vertices of the original figure. Thensubtract 2 from each y-coordinate of the vertices of the original figure.What do you notice?
Read the Lesson3. When translating a figure, what do you know about every point of the
original figure?
4. Can a figure be turned in a translation? Explain.
5. What notation is used to indicate the vertices of a translated figure?
6. Which figure is a translation of Figure 1—Figure 2 or Figure 3? Explain why one figure is a translation and why the other figure is not a translation.
Remember What You Learned7. Describe the translation given by the ordered pair (�7, 3). Think of a way
to remember which direction to translate when the x-coordinate of theordered pair describing the translation is negative.
1
2
3
7MG3.2
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionTranslations
Chapter 10 58 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
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panies, Inc.
10-9
Triangle ABC has vertices A(�4, �2), B(�2, 0), and C(�1, �3).Find the vertices of triangle ABC after a translation of 5 unitsright and 2 units up.
Add 5 to each x-coordinate. Add 2 to each y-coordinate.
The coordinates of the vertices of �ABC are A(1, 0), B(3, 2), and C(4, �1).
1. Translate �GHI 1 unit left and 2. Translate rectangle LMNO 4 units right5 units down. and 3 units up.
Triangle RST has vertices R(3, 2), S(4, �2), and T(1, �1). Find thevertices of RST after each translation. Then graph the figure andits translated image.
3. 5 units left, 1 unit up 4. 3 units left, 2 units downy
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T
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S
y
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R
S
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IG
A translation is the movement of a geometric figure in some direction without turning the figure. Whentranslating a figure, every point of the original figure is moved the same distance and in the samedirection. To graph a translation of a figure, move each vertex of the figure in the given direction. Thenconnect the new vertices.
y
xO
B'
C'
A'
A
B
C
Vertices of �ABCVertices of �ABC (x � 5, y � 2)
A(�4, �2) (�4 � 5, �2 � 2)
B(�2, 0) (�2 � 5, 0 � 2)
C(�1, �3) (�1 � 5, �3 � 2)
A(1, 0)
B(3, 2)
C(4, �1)
Example
Exercises
7MG3.2
NAME ________________________________________ DATE ______________ PERIOD _____
Skills PracticeTranslations
Chapter 10 59 Glencoe California Mathematics, Grade 6
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1. Translate �ABC 5 units left. 2. Translate rectangle RSTU 2 units rightand 5 units up.
3. Translate �DEF 4 units left and 4. Translate trapezoid LMNO 5 units right4 units down. and 3 units down.
Triangle XYZ has vertices X(�4, 5), Y(�1, 3), and Z(�2, 0). Find thevertices of XYZ after each translation. Then graph the figure andits translated image.
5. 5 units down 6. 4 units right, 3 units down
Parallelogram RSTU has vertices R(�1, �3), S(0, �1), T(4, �1), andU(3, �3). Find the vertices of RSTU after each translation. Thengraph the figure and its translated image.
7. 3 units left, 3 units up 8. 1 unit right, 5 units upy
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NAME ________________________________________ DATE ______________ PERIOD _____
PracticeTranslations
Chapter 10 60 Glencoe California Mathematics, Grade 6
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1. Translate rectangle ABCD 3 units right 2. Triangle PQR is translated 3 and 4 units down. Graph rectangle units left and 3 units down.ABCD. Then the translated figure is
translated 6 units right.Graph the resulting triangle.
Triangle EFG has vertices E(1, 1), F(4, � 3), and G(�2, 0). Find thevertices of E�F�G� after each translation. Then graph the figureand its translated image.
3. 3 units left, 2 units down 4. 4 units up
5. SEATS Jatin was given a new seating assignmentin science class. The diagram shows his old seat and his new seat. Describe this translation in words and as an ordered pair.
REASONING The coordinates of a point and its image after atranslation are given. Describe the translation in words and as anordered pair.
6. A(1, �2) → A (3, 4) 7. H(3, 3) → H (�4, 0) 8. Z(�2, �4) → Z(1, �5)
Front of Classroom
OLD
NEW
y
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F
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7MG3.2
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Word Problem PracticeTranslations
Chapter 10 61 Glencoe California Mathematics, Grade 6
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MAPS For Exercises 1–4, use the map at the right. Maple St.
Blonde St.
Dodge St.
Pacific Ave.
Center Rd.
Harrison St.
Kens
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on A
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N
1. Stanley’s school is located at the cornerof Center and Elmwood. The library islocated at the corner of Dodge andDelaware. Describe Stanley’s walk fromschool to the library as an ordered pairof the number of blocks.
2. After he goes to the library, Stanleygoes to his Aunt Jeanne’s house at thecorner of California and Harrison.Describe Stanley’s walk from thelibrary to his aunt’s house as anordered pair of the number of blocks.
3. If a bus picks up passengers at thecorner of New York and Maple anddrives 2 blocks south and 3 blocks west, where does the bus end up?
4. Organizers of a walkathon want to mapout a route that will lead people fromthe corner of Center and Kensington tothe corner of California and Maple.Write a coordinate pair that describesthe most direct route.
5. GEOMETRY The figure shows anoctagon plotted on a coordinate system.The figure is to be translated by 5 unitsleft and 5 units down. Graph thetranslated image of the figure.
y
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6. BANKS Clarissa is waiting in line at the bank. There are several people inline in front of her. Describe the pathClarissa must take to get to the front of the line if each time she moves up in line by one position is considered one unit.
tellers
Clarissa
7MG3.2
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 10 62 Glencoe California Mathematics, Grade 6
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10-9
Chess MovesIn the game of chess, a knight can move several different ways. It can move twospaces vertically or horizontally, then onespace at a 90� angle. It can also move onespace vertically or horizontally, then twospaces at a 90� angle. Several examples of a knight’s moves are indicated on thegrid at the right.
1. Use the diagram at the right. Place a knight or other piece in the square marked 1. Move the knight so that it lands on each of the remaining white squares only once. Mark eachsquare in which the knight lands with 2, then 3, and so on.
2. Use the diagram below. Place a knight or other piece in the squaremarked 1. Move the knight so that it lands on each of the remainingsquares only once. Mark each square in which the knight lands with 2, then 3, and so on.
1
1
7MG3.2
Example
NAME ________________________________________ DATE ______________ PERIOD _____
Spreadsheet ActivityTranslations
Chapter 10 63 Glencoe California Mathematics, Grade 6
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You can use a spreadsheet to determine and graph the ordered pairs of a figure after atranslation.
Quadrilateral ABCD has the vertices A(2, 3), B(�1, 2), C(�2, �3),and D(3, �1). Use a spreadsheet to find the vertices of quadrilateral
A'B'C'D' after a translation 4 units left and 2 units up. Then use the spreadsheet to create a graph of ABCD and A'B'C'D'.
Step 1 Use Column A for the x-coordinates and Column B for the y-coordinates. Enter thenumbers using the formula bar. Then press ENTER to move to the next cell. Be sure toenter the coordinates of the first point again at the end of the list.
Step 2 In cell C1, enter an equals sign followed by �A1�4. Then press ENTER to return the x-coordinate of the new point.
Step 3 In cell D1, enter an equals sign followed by �B1�2. Then press ENTER to return the y-coordinate of the new point.
Step 4 To find the remaining new x-coordinates, click on the bottom right corner of cell C1 anddrag it to cell C5. Click on the bottom right corner of cell D1 and drag it to cell D5 to findthe y-coordinates.
The coordinates of A'B'C'D' are A'(�2, 5), B'(�5, 4), C'(�6, �1), and D'(�1, 1).
Step 5 To graph, highlight columns A and B through row 5. Press the Chart Wizard. Select XY(Scatter) and choose the graph with data points connected by lines. Press NEXT. Selectthe SERIES tab. Press the ADD button. In the X-Values bar, enter �Sheet1!$C$1:$C$5. Inthe Y-Values bar, enter �Sheet1!$D$1:$D$5. Press NEXT, NEXT, FINISH to display the graph.
Quadrilateral QUAD hasvertices Q(�2, 1), U(2, 4),A(3, �3) and D(�1, �1). Usea spreadsheet to find thevertices of Q'U'A'D' after atranslation of 2 units rightand 3 units down. Then use aspreadsheet to graph QUADand Q'U'A'D'.
A B C D E F G H123456789
10111213141516
2-1-23
32
-3-1
-2-5-5-1
54
-11
2 3 -1 5
Sheet 1 Sheet 2 Sheet 3
-8 -6 -4 -2 2 4Series 1Series 2
-4-3-2-10123456
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson Reading GuideReflections
Chapter 10 64 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
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panies, Inc.
10-10
Get Ready for the LessonComplete the Mini Lab at the top of page 558 in your textbook. Writeyour answers below.
1. Describe how you drew the reflection of your classmate’s name.
2. Explain why the line where the geomirror and paper meet is called theline of symmetry.
Read the Lesson3. Is the image of a reflection smaller, larger, or the same size as the
original figure?
4. In Example 4 on page 559, how can you tell that one image is a reflectionof the other across the x-axis?
5. Study the coordinates given in Examples 4 and 5 on page 559. How canyou tell how many units a vertex is away from the x-axis withoutgraphing it? How can you tell how many units a vertex is away from they-axis?
Remember What You Learned6. Work with a partner. Draw and cut out figures of regular polygons.
Demonstrate which regular polygons have lines of symmetry and whichdo not. Mark the lines of symmetry with dashed lines on the models.
7MG3.2
Exercises
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionReflections
Chapter 10 65 Glencoe California Mathematics, Grade 6
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Determine whether each figure has line symmetry. If so, draw alllines of symmetry.
no symmetry
Triangle DEF has vertices D(2, 2), E(5, 4), and F(1, 5). Find the coordinates of the reflected
image. Graph the figure and its reflected image over the x-axis.
Plot the vertices and connect to form �DEF. The x-axis is the line of symmetry. The distance from a point on �DEF to the line of symmetry is the same as the distance from the line of symmetry to the reflected image. The image coordinates are D(2, �2),E(5, �4), and F(1, �5).
For Exercises 1 and 2, determine which figures have line symmetry.Write yes or no. If yes, draw all lines of symmetry.
1. 2.
3. Triangle ABC has vertices A(0, 4), B(2, 1), and C(4, 3). Find thecoordinates of the vertices of ABC after a reflection over the x-axis. Then graph the figure and its reflected image.
y
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E'
D'
D
F'
F E
A type of transformation where a figure is flipped over a line of symmetry is a reflection. To draw thereflection of a polygon, find the distance from each vertex of the polygon to the line of symmetry. Plotthe new vertices the same distance from the line of symmetry but on the other side of the line. Thenconnect the new vertices to complete the reflected image.
Figures that match exactly when folded in half have line symmetry. Each fold line is called a line ofsymmetry. Some figures have more than one line of symmetry.
y
xO
Examples
Example 3
7MG3.2
NAME ________________________________________ DATE ______________ PERIOD _____
Skills PracticeReflections
Chapter 10 66 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
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-Hill, a division of T
he McG
raw-H
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panies, Inc.
10-10
Determine which figures have line symmetry. Then draw all lines ofsymmetry.
1. 2. 3.
4. 5. 6.
Graph the figure and its reflection over the x-axis. Then find thecoordinates of the reflected image.
7. triangle ABC with vertices A(�3, 4),B(1, 4), and C(3, 1)
8. rectangle MNOP with vertices M(�2, �4),N(�2, �1), O(3, �1), andP(3, �4)
Graph the figure and its reflection over the y-axis. Then find thecoordinates of the reflected image.
9. triangle DEF with vertices D(1, 4), 10. trapezoid WXYZ with vertices W(�1, 3),E(4, 3), and F(2, 0) X(�1, �4), Y(�5, �4), and Z(�3, 3)
y
xO
y
xO
y
xO
y
xO
7MG3.2
Determine whether each figure has line symmetry. If so, copy thefigure and draw all lines of symmetry.
1. 2. 3.
4. 5. 6.
7. Graph �ABC with vertices A(2, 2), 8. Graph square ABCD with vertices B(5, 4),and C(5, 1) and its reflection over A( �1, 2), B(2, �1), C(5, 2), and D(2, 5)the x-axis. Then find the coordinates and its reflection over the y-axis. Thenof the reflected image. find the coordinates of the reflected image.
The coordinates of a point and its image after a reflection are given.Describe the reflection as over the x-axis or y-axis.
9. B(1, �2) → B(1, 2) 10. J(�3, 5) → J(�3, �5) 11. W(�7, �4) → W(7, �4)
y
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y
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NAME ________________________________________ DATE ______________ PERIOD _____
PracticeReflections
Chapter 10 67 Glencoe California Mathematics, Grade 6
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NAME ________________________________________ DATE ______________ PERIOD _____
Word Problem PracticeReflections
Chapter 10 68 Glencoe California Mathematics, Grade 6
Copyright ©
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10-10
1. FLAGS The figure shows a flag similarto the national flag of Denmark. Howmany lines of symmetry does the flaghave? Draw all lines of symmetry.
2. FLAGS The figure shows a flag similarto the national flag of Switzerland.How many lines of symmetry does theflag have? Draw all lines of symmetry.
3. INTERIOR DESIGN An interior designerhas been hired to decorate a room thathas the shape of a regular hexagon.Before beginning work, the designerstudies the symmetry of the room. Howmany lines of symmetry does the roomhave? Draw all lines of symmetry onthe figure.
4. ASTROLOGY The figure shows theastrological symbol for Sagittariusplotted on a coordinate system. Reflectthe symbol across the x-axis. Graph thereflected image.
y
xO
5. ARCHITECTURE A corporate plaza is tobe built around a small lake. Building 1has already been built. Suppose thereare axes through the lake as shown.Show where Building 2 should be builtif it will be a reflection of Building 1across the y-axis followed by areflection across the x-axis.
y
xO
Building 1
Lake
6. ARCHITECTURE Use the informationfrom Exercise 5. Suppose that a thirdbuilding is to be built as shown. Tocomplete the business park, showwhere a fourth building should be builtif it is a reflection of Building 3 acrossthe x- and y-axis.
y
xO
Building 1Building 3
Lake
7MG3.2
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 10 69 Glencoe California Mathematics, Grade 6
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The Twelve Dot PuzzleIn this puzzle, a broken line made up of 5 segments must pass through each of 12 dots. The line cannot go through a dot more than once, although it may intersect itself. The line must start at one dot and end at a different dot.
One solution to this puzzle is shown at the right. Two solutions to the puzzle are not “different” if one is just a reflection or rotation of the other.
Find 18 other solutions.
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12.
13. 14. 15.
16. 17. 18.
7MG3.2
Exercises
Example
NAME ________________________________________ DATE ______________ PERIOD _____
TI-73 ActivityLines of Symmetry
Chapter 10 70 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
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10-10
Draw polygons on the calculator by entering the coordinates of the vertices. Use the DRAWfeature to check for vertical and/or horizontal lines of symmetry.
The vertices of a polygon are: (1, 2), (7, 2), (7, 4), (4, 7), and (1, 4). Draw thepolygon and tell whether it has vertical and horizontal lines of symmetry.
Step 1 Clear all lists.
[MEM] 6
Step 2 Enter the x-coordinates in L1. Enter the y-coordinates in L2. Repeat the first value at theend of each column.
Step 3 Create Plot1.
[PLOT] 4
[PLOT] 1
Step 4 Choose L1 and L2, if not already chosen.
[STAT] [STAT]
Step 5 Set the graph window and display the plot.
4
Step 6 Draw a vertical line through the polygon. Use the arrow keys to center the line.
4
This polygon has a vertical line of symmetry.
Draw each polygon on the calculator and find any vertical or horizontal lines ofsymmetry.
1. (1, 5) 2. (10, 3)(4, 1) (6, 6)(4, 9) (2, 3)
3. (5, 3) 4. (2, 6)(1, 1) (4, 1)(8, 1) (7, 1)(12, 3) (9, 6)
DRAW
ZOOM
ENTER2ndENTER2nd
ENTERENTER2nd
ENTER2nd
LIST
ENTER2nd
Pre-AP
NAME ________________________________________ DATE ______________ PERIOD _____
Student Recording SheetUse this recording sheet with pages 568–569 of the Student Edition.
Chapter 10 71 Glencoe California Mathematics, Grade 6
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Read each question. Then fill in thecorrect answer.
1.
2.
3.
4.
5.
6.
7.
8.
9.
Record your answers for Question 10 onthe back of this paper.
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
10
Ass
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General Scoring Guidelines• If a student gives only a correct numerical answer to a problem but does not show how he or she
arrived at the answer, the student will be awarded only 1 credit. All extended response questionsrequire the student to show work.
• A fully correct answer for a multiple-part question requires correct responses for all parts of thequestion. For example, if a question has three parts, the correct response to one or two parts of thequestion that required work to be shown is not considered a fully correct response.
• Students who use trial and error to solve a problem must show their method. Merely showing thatthe answer checks or is correct is not considered a complete response for full credit.
Exercise 10 Rubric
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Chapter 10 72 Glencoe California Mathematics, Grade 6
10 Rubric for Scoring Pre-AP(Use to score the Pre-AP question on page 569 of the Student Edition.)
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Score Specific Criteria4 �J is correctly identified as an obtuse angle, and �M is correctly identified as an
acute angle. The polygon is correctly identified as a parallelogram. An accurateexplanation that the polygon can be used by itself to make a tessellation is given.The coordinates of the translated figure are correctly determined to be J�(�1, 0),K�(�2, �4), L�(0, �4), and M�(1, 0). The coordinates of the reflection are correctlydetermined to be J�(�3, 5), K�(�4, �1), L�(�2, �1), and M�(�1, �5).
3 The identifications and the coordinates of the translation and the reflection arecorrect, but the explanation is not complete or not given. ORThe explanation and the coordinates of the translation and the relection are correct,but one of the identifications is not correct. ORThe identifications and the explanation are correct, but a mistake is made indetermining the coordinates of one or two vertices of the translated or reflectedfigure.
2 The identifications and the explanation are correct, but either the translation or the reflection is incorrect. ORThe explanation, translation, and reflection are corrrect, but two or three of theidentifications are incorrect.
1 The identifications are correct, but the explanation, translation, and reflection areincorrect. ORThe explanation is correct, but the identifications, translation, and reflection areincorrect. ORThe translation is correct, but the identifications, explanation, and reflection areincorrect. ORThe reflection is correct, but the identifications, explanation, and translation areincorrect.
0 Response is completely incorrect.
1. The circle graph showshow Enzo spends his day.Which activity does he spend most of his time doing? 1.
Classify each pair of angles as complementary, supplementary,or neither.
2. 3. 2.
3.
Label the angles as vertical or adjacent.4. 5. 4.
5.3 42
1
145˚35˚
53˚37˚
Daily Activities
20%Entertainment
30%Sleeping20%
Working
10%Eating
5%Dining 15%
Other
Find the missing measure in each triangle. Then classifythe triangle as acute, right, or obtuse.
1. 2. 1.
2.
ALGEBRA Find the missing angle measure in each quadrilateral.
3. 4. 3.
4.
5. MULTIPLE CHOICE The first three rows in a theater have 24 seats, 28 seats, and 34 seats, respectively.If the fifth row has 52 seats, how many seats does the fourth row have?A. 38 B. 40 C. 42 D. 0 5.
114˚
73˚
112˚
x˚50˚
x˚
23˚
29˚x˚
55˚
62˚
x˚
Chapter 10 73 Glencoe California Mathematics, Grade 6
Chapter 10 Quiz 1(Lessons 10-1 through 10-3)
Chapter 10 Quiz 2(Lessons 10-4 through 10-6)
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NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
10
10
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1. A photo that is 3 inches wide by 6 inches long will be resized to fit in a space that is 2 inches wide. How long will the resized photo be? 1.
Find the value of x in each pair of similar figures.
2. 3. 2.
3.Determine whether each figure is a polygon. If it is,classify the polygon and state whether it is regular. 4.If it is not a polygon, explain why.
4. 5. 5.
9 cm
2 cm
x3 cm
6 ft
3 ft1.5 ftx
1. Triangle ABC with vertices A(2, 4), B(3, �2), and C(�5, 1) 1.is translated 4 units left and 3 units up. What are the coordinates of B�?
2. Quadrilateral DEFG has vertices D(3, �1), E(7, �1), 2.F(8, �4), and G(1, �3). Find the vertices of D�E�F�G�after a translation of 2 units left and 6 units up.
3. Determine whether the figure at the right has line symmetry. Write yes or no. If yes, then draw all lines of symmetry. 3.
4. Triangle XYZ has vertices X(�10, 4), Y(�8, �2), and Z(�6, 0). 4.It is reflected over the x-axis. What are the coordinates of X�?
5. Parallelogram ABCD has vertices A(�3, 2), B(�1, 4),C(�1, �1), and D(�3, �3). Graph the figure and its reflection over the y-axis. Then find the coordinates of its reflected image.
5.
Chapter 10 74 Glencoe California Mathematics, Grade 6
Chapter 10 Quiz 3(Lessons 10-7 and 10-8)
Chapter 10 Quiz 4(Lessons 10-9 and 10-10)
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
10
10
Copyright ©
Glencoe/M
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he McG
raw-H
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panies, Inc.
y
xO
Write the letter for the correct answer in the blank at the right of each question.
1. MONEY The following circle graph shows where the United States government spends its money.On what do they spend the most money?A. Interest on Public Debt C. DefenseB. Social Security D. Health 1.
2. Angle 1 and angle 2 are supplementary.If m�1 � 27�, find m�2.F. 27� H. 73�
G. 63� J. 153� 2.
3. Determine which property is not a characteristic of a trapezoid.A. one pair of parallel sides C. need not have a right angleB. quadrilateral D. 4 congruent sides 3.
Classify each angle as acute, right, obtuse, or straight.
4. 5. 6. 4.
5.
6.Classify each pair of angles as supplementary,complementary, or neither.
7. 8. 7.
8.
Classify each triangle by its angles and by its sides.
9. 10. 9.
10.
Classify each quadrilateral using the name that best describes it.
11. 12. 11.
12.
48˚48˚110˚70˚
U.S. Money Expenditures
22%Interest
on PublicDebt
21%Health
16%Defense(Military)
16%Other
25%Social
Security
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Chapter 10 75 Glencoe California Mathematics, Grade 6
10NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 10 Mid-Chapter Test(Lessons 10-1 through 10-6)
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Copyright ©
Glencoe/M
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panies, Inc.
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Chapter 10 76 Glencoe California Mathematics, Grade 6
10 Chapter 10 Vocabulary Test
Choose the correct term to complete each sentence.
1. Degrees are the unit of measure for (angles, lengths). 1.
2. Two angles are (complementary, supplementary) angles if 2.the sum of their measures equals 90�.
3. A scalene triangle has (two, no) congruent sides. 3.
4. A rhombus is a parallelogram with (four, two) congruent sides. 4.
5. A pentagon is a polygon with (six, five) sides. 5.
6. A (tessellation, transformation) is a repetitive pattern of 6.polygons that fit together with no overlaps or holes.
7. A line of symmetry is used with a (translation, reflection). 7.
8. An (acute, obtuse) angle has a measure between 90� and 180�. 8.
9. Congruent angles have the same (sides, measure). 9.
10. A polygon is formed by (three, two) or more straight lines. 10.
Define each term in your own words.
11. parallel
12. indirect measurement
acute angle anglecircle graphcomplementary anglescongruent anglescongruent figuresdegreeshexagonindirect measurementline of symmetry
line symmetryobtuse angleoctagonparallelogrampentagonpolygonquadrilateralreflectionregular polygonrhombus
right anglesimilar figuresstraight anglesupplementary anglestessellationtransformationtranslationtrapezoidtrianglevertex
Write the letter for the correct answer in the blank at the right of each question.
1. The measure of an angle is 45�. Classify the angle.A. acute B. straight C. obtuse D. right 1.
2. ALGEBRA If �P and �Q are complementary and the measure of �P is 40°,what is the measure of �Q?F. 40° G. 50° H. 60° J. 140° 2.
3. What is the angle measure for a section in a circle graph that represents 25%?A. 9° B. 25° C. 90° D. 335° 3.
4. OLYMPICS The table shows the results of a student survey. On a circle graph of the data, which section would have an angle measure of 180�?F. Bobsled H. SkiingG. Skating J. Curling 4.
For Questions 5 and 6, classify each pair of angles.
5. 6. 5.
A. complementary F. complementaryB. supplementary G. supplementaryC. right H. rightD. no relationship J. no relationship 6.
7. Which figure is a polygon? A. B. C. D. 7.
8. Which figure is a regular polygon?F. G. H. J. 8.
9. Which pair of figures is similar?A. B. C. D. 9.
10. Find the value of x in the pair of similar figures.F. 4 H. 2G. 3 J. 1 10.
1234˚ 146˚
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Chapter 10 77 Glencoe California Mathematics, Grade 6
10NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 10 Test, Form 1C
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Favorite WinterOlympic Events
Number of Students
Bobsled 12Skating 30Skiing 45Curling 3
7
3 4
546
3 2
3
4
23
13
53
663 3
4 2
6 cmx cm
2 cm
1 cm
11. Classify the quadrilateral using the name that best describes it.A. square C. trapezoidB. parallelogram D. rhombus 11.
12. Classify the triangle by its angles and by its sides.F. acute, equilateral H. obtuse, isoscelesG. right, equilateral J. obtuse, equilateral 12.
13. Classify the quadrilateral using the name that best describes it.A. rhombus C. squareB. rectangle D. trapezoid 13.
14. Which regular polygon can be used by itself to make a tessellation?F. pentagon G. octagon H. square J. decagon 14.
15. Find the coordinates of J� after �HIJ is translated 2 units down.A. (2, 4) C. (0, 5)B. (0, 2) D. (2, 3) 15.
16. Parallelogram ABCD with vertices A(�5, 2), B(�4, 4),C(�1, 4), and D(�2, 2) is translated 3 units right and 4 units up. What are the coordinates of A�?F. (�8, �2) G. (�2, 6) H. (2, 6) J. (3, 4) 16.
17. Find the coordinates of �T�U�V� with vertices T(2, 2), U(5, 4), V(5, 2) after a reflection over the y-axis.A. T�(�2, 2), U�(�5, 4), V�(�5, 2) C. T�(2, 2), U�(4, 5), V�(2, 5)B. T�(2, �2), U�(5, �4), V�(5, �2) D. T�(2, �2), U�(5, �4), V�(�5, �2) 17.
18. Choose the figure that shows all lines of symmetry drawn correctly.F. G. H. J. 18.
19. ART An artist is using right triangles in her design. If all the triangles have an angle measure of 24°, what is the measure of the third angle? A. 66° B. 76° C. 106° D. 156° 19.
20. BOOKS Brooke, Mia, and Orlando are reading a mystery, fiction, and comic book, but not in that order. Mia does not care for fiction books.Orlando does not read fiction or comic books. Which is a true pairing? F. Brooke, fiction H. Mia, fictionG. Brooke, mystery J. Orlando, comic book 20.
Bonus Name the regular polygon if the sum of the measures of the polygon is 1,440� and the measure of one angle is 144�. B:
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NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 78 Glencoe California Mathematics, Grade 6
10 Chapter 10 Test, Form 1 (continued)C
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lencoe/McG
raw-H
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ompanies, Inc.
Write the letter for the correct answer in the blank at the right of each question.
1. The measure of an angle is 95�. Classify the angle.A. acute B. right C. straight D. obtuse 1.
2. ALGEBRA If �W and �X are complementary and the measure of �W is 56°,what is the measure of �X?F. 34° G. 44° H. 104° J. 124° 2.
3. What is the angle measure for a section in a circle graph that represents 38%?A. 38° B. 68° C. 137° D. 322° 3.
4. OLYMPICS The table shows the results of a student survey. On a circle graph of the data, which section would have an angle measure of 48�?F. Bobsled H. SkiiingG. Skating J. Curling 4.
For Questions 5 and 6, classify each pair of angles.
5. 6. 5.
A. complementary F. complementaryB. supplementary G. supplementaryC. right H. rightD. no relationship J. no relationship 6.
7. Which figure is a polygon? A. B. C. D. 7.
8. Which figure is a regular polygon? F. G. H. J. 8.
9. Choose the pair of similar figures.A. B. C. D. 9.
10. Find the value of x in the pair of similar figures.F. 1.5 H. 2.5G. 2 J. 3 10.5 m
2 m 2 m 1 m1.5 m1.5 m
1 m
3 m 3 m
x m
2
8 4
1
69 5 4
34
4
52
13
10
5
12
12
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Chapter 10 79 Glencoe California Mathematics, Grade 6
10NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 10 Test, Form 2AC
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BobsledSkatingSkiingCurling
Number ofStudents
Favorite WinterOlympic Events
3453012
136
4
11. Classify the quadrilateral using the name that best describes it.A. rhombus C. parallelogramB. square D. trapezoid 11.
12. Classify the triangle by its angles and by its sides.F. right, isosceles H. obtuse, isoscelesG. acute, isosceles J. acute, equilateral 12.
13. Classify the quadrilateral using the name that bestdescribes it.A. square C. parallelogramB. trapezoid D. rectangle 13.
14. Which regular polygon can be used by itself to make a tessellation?F. octagon H. equilateral triangleG. decagon J. circle 14.
15. Find the coordinates of H�after �HIJ is translated 5 units down.A. (�3, 5) C. (�8, �1)B. (�6, �3) D. (�3, �6) 15.
16. Parallelogram ABCD with vertices A(�3, �1), B(2, �1), C(1, �3), andD(�4, �3) is translated 4 units left and 8 units up. What are thecoordinates of C�?F. (�4, 8) G. (�3, 5) H. (�5, 5) J. (5, �3) 16.
17. Find the coordinates of �T�U�V� with vertices T(�1, 2), U(1, �1),V(�3, �2) after a reflection over the x-axis.A. T�(�1, �2), U�(1, 1), V�(�3, 2) C. T�(1, 2), U�(�1, �1), V�(3, �2)B. T�(1, �2), U�(�1, 1), V�(3, 2) D. T�(2, �1), U�(�1, 1), V�(�2, �3) 17.
18. Choose the figure that shows all lines of symmetry drawn correctly.F. G. H. J. 18.
19. ART An artist is using right triangles in her design. If all the triangles have an angle measure of 68�, what is the measure of the third angle? A. 22� B. 32� C. 112� D. 122� 19.
20. BOOKS Brenna, Leslie, John, and Wesley are reading a mystery (M),fiction (F), biography (B), and comic book (C), but not in that order. Brennadoes not like mystery, fiction, or comic books. Neither Leslie nor John likesmysteries. Leslie does not like comic books. Which is a true pairing? F. Brenna (F) G. Leslie (M) H. John (C) J. Wesley (B) 20.
Bonus Name the regular polygon if the sum of the measures of the polygon is 3,240� and the measure of one angle is 162�. B:
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 80 Glencoe California Mathematics, Grade 6
10 Chapter 10 Test, Form 2A (continued)C
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lencoe/McG
raw-H
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cGraw
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ompanies, Inc.
y
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I J
Write the letter for the correct answer in the blank at the right of each question.
1. The measure of an angle is 89�. Classify the angle.A. acute B. right C. straight D. obtuse 1.
2. ALGEBRA If �M and �N are supplementary and the measure of �M is 74�, what is the measure of �N?F. 16° G. 26° H. 106° J. 126° 2.
3. What is the angle measure for a section in a circle graph thatrepresents 47%?A. 47° B. 85° C. 169° D. 313° 3.
4. OLYMPICS The table shows the results of a student survey. On a circle graph of the data, which section would have an angle measure of 120�?F. Bobsled H. SkiingG. Skating J. Curling 4.
For Questions 5 and 6, classify each pair of angles.
5. 6. 5.
A. complementary F. complementaryB. supplementary G. supplementaryC. right H. rightD. no relationship J. no relationship 6.
7. Which figure is a polygon?A. B. C. D. 7.
8. Which figure is not a regular polygon? F. G. H. J. 8.
9. Choose the pair of similar figures.A. B. C. D. 9.
10. Find the value of x in the pair of similar figures.F. 1.5 H. 3.5G. 3 J. 14 10.
4
2
5
3
27 3
14 2510
12
21
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Chapter 10 81 Glencoe California Mathematics, Grade 6
10NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 10 Test, Form 2BC
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Favorite WinterOlympic Events
Number ofStudents
Bobsled 12Skating 30Skiing 45Curling 3
117
9
35
4
7 m
2 m
2 m6 m
6 m 1 m
1 m3 m3 m x m
11. Classify the quadrilateral using the name that best describes it.
A. quadrilateral B. rhombus C. trapezoid D. parallelogram 11.
12. Classify the triangle by its angles and by its sides.F. obtuse, scalene G. right, isosceles H. right, scalene J. acute, scalene 12.
13. Classify the quadrilateral using the name that best describes it.A. trapezoid C. parallelogramB. rhombus D. square 13.
14. Which regular polygon can be used by itself to make a tessellation?F. octagon G. hexagon H. heptagon J. circle 14.
15. Find the coordinates of I� after �HIJ is translated 5 units down.A. (�1, �2) C. (�2, �2)B. (�2, 2) D. (�2, �1) 15.
16. Parallelogram ABCD with vertices A(�3, �1), B(2, �1),C(1, �3), and D(�4, �3) is translated 4 units left and 8 units up. What are the coordinates of B�?F. (�2, 7) G. (�2, 8) H. (2, 9) J. (10, �5) 16.
17. Find the coordinates of �T�U�V� with vertices T(�1, 2), U(1, �1), V(�3, �2) after a reflection over the y-axis.A. T�(�1, �2), U�(�1, �1), V�(�3, 2) C. T�(�1, �2), U�(1, 1), (�3, 2)B. T�(2, �1), U�(�1, 1), (�2, �3) D. T�(1, 2), U�(�1, �1), (3, �2) 17.
18. Choose the figure that shows all lines of symmetry drawn correctly.F. G. H. J. 18.
19. ART An artist is using right triangles in her design. If all the triangles have an angle measure of 58�, what is the measure of the third angle? A. 22° B. 32� C. 112� D. 122� 19.
20. BOOKS Brenna, Leslie, John, and Wesley are reading a mystery, fiction,biography, and comic book, but not in that order. Wesley does not likemystery, fiction, or comic books. Neither Leslie nor John likes mysteries.Leslie does not like comic books. Which is a true pairing? F. Brenna, fiction H. John, fictionG. Leslie, biography J. Wesley, biography 20.
Bonus Name the regular polygon if the sum of the measures of the polygon is 2,520� and the measure of one angle is 157.5�. B:
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NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 82 Glencoe California Mathematics, Grade 6
10 Chapter 10 Test, Form 2B (continued)C
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1. Draw an angle having a measurement of 180�. Then classify 1.the angle as acute, obtuse, right, or straight.
For Questions 2 and 3, name each angle in four ways. Then classify the angle as acute, right, obtuse, or straight. 2.
2. 3.
3.
4. MONEY For the following table, find the number of degrees for each section of a circle graph. Then make a circle graph of the data.
5. ALGEBRA If �R and �S are complementary and �S is 82°,what is the measure of �R? 4.
6. Find the value of x in the figure. 5.
6.
Find the value of x.
7. 8. 7.
8.
Classify each quadrilateral using the name that bestdescribes it.
9. 10. 9.
10.
11. Find the missing angle measure. 11.147˚
40˚ 90˚
x˚
37˚
53˚
x˚
28˚
35˚
x˚
98˚x˚
Bills in Circulation
JK
L2
B
A
C1
Ass
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Chapter 10 83 Glencoe California Mathematics, Grade 6
10NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 10 Test, Form 2CC
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Bobsled 12Bobsled12
Type of Bills Number of Bills inCirculation (trillions)
$1 bills 6$5 bills 1
$10 bills 1$20 bills 4
12. Determine whether the pair of figures is
similar. Justify your answer. 12.
13. Find the value of x in thepair of similar figures. 13.
For Quesions 14 and 15, find the 14.measure of an angle in each polygon.
14. regular pentagon 15. regular octagon 15.
16. Triangle ABC has vertices A(1, 2), B(�2, 3), and C(0, �3).Find the vertices of �A�B�C� after a translation of 4 units right and 2 units up. Then graph the figure and its translated image. 16.
17. Point W (1, 3) is reflected to its image W� (1, �3). Describe the reflection as over the x-axis or y-axis. 17.
18. Draw all lines of symmetry for an equilateral triangle. 18.
19. ALGEBRA Find m�G in �FGH if m�F � 47° and m�H � 65°. 19.
20. FOOD For lunch Avery, Nathan, Alex, and Takara ordered tacos, a salad, fish sandwich, and pasta, but not in that order.Nathan does not like fish, tacos, or salad. Neither Alex nor Takara likes fish. Takara does not like tacos. Find the food that each person ordered. 20.
Bonus Can a regular polygon with an angle measure of 160� be used by itself to make a tessellation? Explain. B:
y
xO
4 ft6 ft 2 ft 3 ft
4 ftx ft
1 m 2 m
5 m
3 m
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 84 Glencoe California Mathematics, Grade 6
10 Chapter 10 Test, Form 2C (continued)C
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lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
1. Draw an angle having a measurement of 90�. Then classify the angle as acute, obtuse, right, or straight. 1.
For Questions 2 and 3, name each angle in four ways. Then classify the angle asacute, right, obtuse, or straight.
2. 3. 2.
3.
4. MONEY For the following table, find the number of degrees for each section of a circle graph. Then make a circle graph of the data.
5. ALGEBRA If �C and �D are supplementary and �D is 70°,
4.
what is the measure of �C? 5.
6. Find the value of x in the figure. 6.
Find the value of x.
7. 8. 7.
8.
Classify each quadrilateral using the name that bestdescribes it.
9. 10. 9.
10.
11. Find the missing angle measure. 11.
80˚
100˚
135˚x˚
42˚48˚
x˚88˚
29˚ x˚
46˚x˚
Bills in CirculationQ
R
S4
F
GH
3
Ass
essm
ent
Chapter 10 85 Glencoe California Mathematics, Grade 6
10NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 10 Test, Form 2DC
opyr
ight
©G
lenc
oe/M
cGra
w-H
ill,
a di
visi
on o
f The
McG
raw
-Hill
Com
pani
es,
Inc.
Type of Bills Number of Bills inCirculation (trillions)
$5 bills 1$10 bills 1$20 bills 4
$100 bills 3
12. Determine whether the pair of figures is similar. Justify your answer.
12.
13. Find the value of x in the 13.pair of similar figures.
For Questions 14 and 15, find the measure of an angle in each polygon. 14.
14. regular hexagon 15. regular nonagon 15.
16. Triangle ABC has vertices A(1, 2), B(�2, 3), and C(0, �3).Find the vertices of �A�B�C� after a translation of 2 units left and 3 units up. Then graph the figure and its translated 16.image.
17. Point X(3, 5) is reflected to its image X�(�3,5). Describe the reflection as over the x-axis or y-axis. 17.
18. Draw all lines of symmetry for a square. 18.
19. ALGEBRA Find m�S in�STU if m�T � 59° and m�U � 70°. 19.
20. FOOD For lunch Avery, Nathan, Alex, and Takara ordered tacos, salad, fish sandwich, and pasta, but not in that order.Avery does not like fish, tacos, or salad. Neither Alex nor Takara likes fish. Takara does not like tacos. Find the food that each person ordered. 20.
Bonus Can a regular polygon with an angle measure of 135� be used by itself to make a tessellation? Explain. B:
y
xO
6 cm 4 cm
x
2 cm3 cm
2.5 cm
5 ft
3 ft
1 ft
3 ft
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 86 Glencoe California Mathematics, Grade 6
10 Chapter 10 Test, Form 2D (continued)C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
1. Draw an angle having a measurement of 147�. Then classifythe angle as acute, obtuse, right, or straight. 1.
For Questions 2 and 3, name each angle in four ways.Then classify the angle as acute, right, obtuse, or straight.
2. 3. 2.
3.
4. MONEY For the following table, find the number of degrees for each section of a circle graph. Then make a circle graph of the data.
5. ALGEGBRA If �A and �B are supplementary and m�A�108.5°, 5.what is m�B?
6. Find the value of x in the figure. 6.
Find the value of x.
7. 8. 7.
8.
Classify each quadrilateral using the name that bestdescribes it.
9. 10. 9.
10.
11. Find the missing angle measure. 11.110˚ x˚
37˚ 32˚
x˚
37˚x˚
76˚
x˚
Bills in Circulation
C
E
D
6L
M N
5
Ass
essm
ent
Chapter 10 87 Glencoe California Mathematics, Grade 6
10NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 10 Test, Form 3C
opyr
ight
©G
lenc
oe/M
cGra
w-H
ill,
a di
visi
on o
f The
McG
raw
-Hill
Com
pani
es,
Inc.
Type of Bills Number of Bills inCirculation (billions)
$1 bills 6,400
$2 bills 600
$5 bills 1,500
$10 bills 1,300
$20 bills 4,100
$50 bills 900
$100 bills 2,900 4.
12. Determine whether the pair 12.of figures is similar. Justify your answer.
13. Find the value of x in the pair 13.of similar figures.
For Questions 14 and 15, find the measure of an angle in each polygon. 14.
14. regular decagon 15. regular 18-gon 15.
16. Triangle ABC has vertices A(1, 2), B(�2, 3), and C(0, �4).The vertices of �A�B�C� after a translation are A�(�3, 5),B�(�6, 0), and C�(�4, �1). Describe the translation. 16.
17. Parallelogram WXYZ has vertices W(�1, 2), X(3, 2),Y(1, �1), and Z(�3, �1). Graph the figure and its reflected image over the y-axis. Then find the coordinates of the reflected image. 17.
18. Draw all lines of symmetry for a regular pentagon. 18.
19. ALGEBRA Find m�S in �STU if m�T � 19.8°and m�U � 65.4°. 19.
20. SPORTS Avery, Nathan, Alex, and Takara are on the following teams: basketball, swimming, soccer, and gymnastics, but not necessarily in that order. Neither Alex nor Nathan do gymnastics. Takara holds a record in swimming. Alex may play soccer next year. Who is on which team? 20.
Bonus Can a regular polygon with an angle measure of 120° be used by itself to make a tessellation? Explain. B:
y
xO
1 ft4 ft
3 ft
0.5 ft 2 ft0.75 ft
1.5 ftx
6 mm3 mm
5 mm2 mm
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 88 Glencoe California Mathematics, Grade 6
10 Chapter 10 Test, Form 3 (continued)C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
Demonstrate your knowledge by giving a clear, concise solution toeach problem. Be sure to include all relevant drawings and justifyyour answers. You may show your solutions in more than one way orinvestigate beyond the requirements of the problem. If necessary,record your answer on another piece of paper.
1. a. Draw a figure that is a polygon and another figure that is not apolygon. Explain how the figures are different.
b. Explain how to classify triangles by the measure of their angles. Drawan example of each classification.
c. Describe at least four classifications of quadrilaterals. Draw anexample of each.
d. Is a trapezoid ever a rhombus? Explain your reasoning.
e. Explain what is meant by regular polygon.
f. Draw a right angle, obtuse angle, straight angle, and acute angle.Explain how the figures are different.
g. Draw an example of supplementary angles. Explain howsupplementary angles are different from complementary angles.
2. a. Explain why you think honeycombs are tessellated with hexagonsinstead of octagons.
b. Tile a rectangular area with squares. Then use at least twotranslations to create an Escher-like drawing. Explain each step.
3. a. Draw a figure that has two or more lines of symmetry. Draw all thelines of symmetry.
b. Draw a figure that has no lines of symmetry.
135˚135˚
90˚
120˚
120˚120˚
Ass
essm
ent
Chapter 10 89 Glencoe California Mathematics, Grade 6
10NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 10 Extended-Response Test
Cop
yrig
ht ©
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ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
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w-H
ill C
ompa
nies
, In
c.
1. GEOMETRY What is the area of the rectangle? (Lesson 3-6)
A 5 m2 C 7.14 m2
B 6.5 m2 D 13 m2 1.
2. Write �383�
as a decimal using bar notation. (Lesson 4-5)
F 24.2�4� G 0.24� H 0.2�4� J 0.2�4�2� 2.
3. Find 3�13� � 3�
29�. Write in simplest form. (Lesson 5-3)
A 6�14� B 6�
13� C 6�
59� D 7�
29� 3.
4. Write �23� as a percent to the nearest hundredth. (Lesson 6-8)
F 0.67% G 1.67% H 66.33% J 66.67% 4.
5. Estimate 26% of 319. (Lesson 7-3)
A 100 B 80 C 32 D 8 5.
6. COLLECTIONS Jamilla bought six new frog figurines to add to her collection. This is 24% of the previous number she originally owned. How many figurines did she originally have in her collection? (Lesson 7-5)
F 25 G 24 H 18 J 15 6.
7. What is the range of the data in the line plot?(Lessons 8-1)
A 45 C 15B 44.8 D 9 7.
8. ATTENDANCE The following set of data lists the number of students in the seventh-grade classes at Smith Valley Middle School: 25, 22, 23, 18, 21, 17. Find the median of the number of students in the seventh-grade classes. (Lesson 8-2)
F 20 G 20.5 H 21 J 21.5 8.
9. WEATHER The probability that it rains today is �1285�. Find
the probability that it will not rain today. (Lesson 9-2)
A 7% B 18% C 28% D 72% 9.
10. CLOTHES Bob bought 2 button-down shirts, 3 ties, 2 pairs of socks, and 3 pairs of pants. How many different outfits can Bob make with his new clothes, choosing one of each? (Lesson 9-3)
F 36 G 15 H 10 J 4 10. F G H J
A B C D
F G H J
A B C D
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Part 1: Multiple Choice
Instructions: Fill in the appropriate oval for the best answer.
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Chapter 10 90 Glencoe California Mathematics, Grade 6
10 Standardized Test Practice(Chapters1–10)
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
1.4 m
5.1 m
11. DECORATING How many different ways can 7 different candles be arranged in a line on a shelf? (Lesson 9-4)
A 42 C 5,040 B 840 D 40,320 11.
12. Out of 20 rolls of a number cube, Mark rolls a 4 five times.What is the experimental probability of rolling a 4? (Lesson 9-7)
F �210� H �
14�
G �15� J �
45� 12.
13. The measure of an angle is 135�. Classify the angle.(Lesson 10-1)
A acute C obtuseB straight D right 13.
14. SCHOOL Sam has his own small chalkboard similar in shape to the one at school. Find the missing measurement of Sam’s chalkboard. (Lesson 10-7)
F 1.1 H 2.2G 2 J 3.3 14.
15. Use the graph to tell what type of transformation is shown.(Lessons 10-9 and 10-10)
A translationB reflection over the x-axisC reflection over the y-axisD no movement 15.
16. How many ways can Antoine choose 3 music boxes from a collection of 20? (Lesson 9-5)
F 6 H 123G 60 J 1,140 16.
17. Find the third angle of a right triangle if the measure of one of the angles is 55°. (Lesson 10-4)
A 125 C 45B 80 D 35 17. A B C D
F G H J
A B C D
y
xOL'
M'
L
N'
MN
F G H J
4.4 ft
12.8 ft3.2 ftftx
A B C D
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A B C D
Chapter 10 91 Glencoe California Mathematics, Grade 6
Ass
essm
ent
10NAME ________________________________________ DATE ______________ PERIOD _____
Standardized Test Practice (continued)
(Chapters 1–10)
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
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sion
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w-H
ill C
ompa
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c.
18. Find �35 (�5). (Lesson 2-8) 18.
19. Write the ratio 15.5 per 100 as a percent. (Lesson 4-6) 19.
20. Solve the proportion �35
� � �1x8�. (Lesson 6-4) 20.
21. FURNITURE Find the total price to the nearest cent of an office chair that costs $165 with a sales tax of 7%. (Lesson 7-8) 21.
22. Make a line plot of laundry detergent prices: 22.$5.50, $8.50, $7, $6, $5.50, $8, $6. (Lesson 8-1)
23. Omari’s assignment for art class is to complete 4 projectsfrom a list of 6. In how many ways can Omari do this if theorder in which he does them is not important? (Lesson 9-5) 23.
24. Classify the quadrilateral using the namethat best describes it. (Lesson 10-6) 24.
25. Triangle XYZ has vertices X(2, �1), Y(4, �3), and Z(1, �4). The translated figure �X�Y�Z� has vertices X�(�1, 4), Y�(1, 2), and Z�(�2, 1). (Lesson 10-9)
a. Graph the figure and its translated image. 25a.
b. Describe the translation. 25b.
c. Write the translation as an ordered pair. 25c.
y
xO
Part 2: Short Response
Instructions: Write answers to short response in the space provided.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 10 92 Glencoe California Mathematics, Grade 6
11 Standardized Test Practice (continued)
(Chapters 1–10)
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
An
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10
Chapter Resources
Answers (Anticipation Guide and Lesson 10-1)
Chapter 10 A1 Glencoe California Mathematics, Grade 6
NA
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____
____
____
____
____
____
____
____
____
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Lesson 10–1
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180°
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270°
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Stud
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An
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Cha
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10
10G
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alifo
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6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-1
Cla
ssif
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ch a
ngl
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acu
te,o
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se,r
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aig
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A.
Th
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B.
than
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,so
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1.2.
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Lab
el t
he
angl
es v
erti
cal
or a
dja
cen
t.
5.6.
7.8.
7 8
6
5
3
41
2
34
1 2
•A
n an
gle
has
two
side
s th
at s
hare
a c
omm
on e
ndpo
int.
The
poi
nt w
here
the
sid
es m
eet
is c
alle
d th
eve
rtex
.Ang
les
are
mea
sure
d in
deg
rees
,whe
re 1
deg
ree
is o
ne o
f 36
0 eq
ual p
arts
of
a ci
rcle
.
•A
ngle
s ar
e cl
assi
fied
acco
rdin
g to
the
ir m
easu
re.
•Tw
o an
gles
are
ver
tica
lif
they
are
opp
osite
ang
les
form
ed b
y th
e in
ters
ectio
n of
tw
o lin
es.
•Tw
o an
gles
are
ad
jace
nt
if th
ey s
hare
a c
omm
on v
erte
x, a
com
mon
sid
e, a
nd d
o no
t ov
erla
p.
Righ
t Ang
leAc
ute
Angl
eOb
tuse
Ang
leSt
raig
ht A
ngle
Exam
ple
1
Exam
ple
2
Exer
cise
s
ob
tuse
rig
ht
acu
test
raig
ht
Th
e an
gle
is g
reat
erth
an 9
0°,s
o it
is
anob
tuse
an
gle.
adja
cen
t
Th
ese
angl
es a
read
jace
nt
beca
use
th
eysh
are
a co
mm
on v
erte
x,a
com
mon
sid
e,an
d do
not
ove
rlap
.
�1
and
�3
are
verti
cal a
ngle
s.�
4 an
d �
2 ar
e ve
rtica
l ang
les.
�5
and
�6
are
adja
cent
ang
les
1 32
45
6
vert
ical
vert
ical
adja
cen
t
6MG
2.1
Answers (Lesson 10-1)
Chapter 10 A2 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Wor
d Pr
oble
m P
ract
ice
An
gle
Rel
atio
nsh
ips
Cha
pter
10
13G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–1
pygp
10-1
1.C
LOC
KS
Th
e ti
me
show
n o
n t
he
cloc
k is
11:
05.S
tart
ing
at t
his
tim
e,ap
prox
imat
ely
wh
at t
ime
wil
l it
be
wh
en t
he
han
ds f
orm
an
obt
use
an
gle?
11:1
5
2.A
IRPO
RT
Th
e ru
nw
ays
at a
loc
al
airp
ort
are
sket
ched
in
th
e fi
gure
.C
lass
ify
�1
and
�2
as a
cute
,obt
use
,ri
ght,
or s
trai
ght.
�1
is o
btu
se;�
2 is
acu
te
21
3.FO
UR
SQ
UA
RE
Lau
ren
,Jam
es,L
isa,
and
Lau
rett
a w
ere
play
ing
fou
r sq
uar
e.W
hic
h s
tude
nts
are
sta
ndi
ng
at
vert
ical
an
gles
fro
m o
ne
anot
her
?
Lau
ren
an
d L
aure
tta;
Jam
es
and
Lis
a
Laur
enJa
mes
Lisa
Laur
etta
4.C
LOC
KS
Th
e ti
me
show
n o
n t
he
cloc
k is
12:0
7.A
fter
20
min
ute
s h
ave
gon
e by
,w
ill
the
angl
e fo
rmed
by
the
hou
r an
dm
inu
te h
ands
be
acu
te,o
btu
se,r
igh
t,or
str
aigh
t?
ob
tuse
5.B
ALL
ETW
hen
a b
alle
t da
nce
r’s
feet
are
in f
irst
pos
itio
n,t
he
hee
ls a
re t
ouch
ing,
and
the
feet
are
tu
rned
ou
t.A
dan
cer
wit
h e
xcel
len
t te
chn
iqu
e ca
n p
osit
ion
his
or
her
fee
t so
th
at t
hey
are
nea
rly
in a
str
aigh
t li
ne.
Isab
ella
is
prac
tici
ng
her
tec
hn
iqu
e.C
lass
ify
the
angl
e h
erfe
et f
orm
as
acu
te,o
btu
se,o
r ri
ght.
ob
tuse
6.PA
RK
ING
LO
TE
ric,
Rya
n,A
ish
a,an
d A
bbey
are
all
par
ked
in t
he
sch
ool
lot.
Wh
o is
par
ked
at a
djac
ent
angl
es f
rom
one
anot
her
?
Eri
c an
d R
yan
;R
yan
an
d
Ab
bey
;A
bb
ey a
nd
Ais
ha;
Ais
ha
and
Eri
c
Aish
a
Ryan
Eric
Abbe
y
6MG
2.1
Nam
e ea
ch a
ngl
e in
fou
r w
ays.
Th
en c
lass
ify
the
angl
e as
acu
te,r
igh
t,ob
tuse
,or
stra
igh
t.
1.2.
3.
�4,
�S
,�R
ST
,�
2,�
Y,�
XY
Z,
�1,
�B
,�C
BA
,�
TS
R;
ob
tuse
�Z
YX
;ri
gh
t�
AB
C;
stra
igh
t
4.5.
6.
�3,
�F
,�H
FG
,�
7,�
P,�
JPM
,�
6,�
D,�
ED
F,�
GF
H;
acu
te
�M
PJ;
acu
te�
FD
E;
rig
ht
Use
th
e fi
gure
at
the
righ
t to
an
swer
Qu
esti
ons
7 an
d 8
.
7.N
ame
two
angl
es t
hat
are
ver
tica
l.�
MP
L,�
NP
O o
r �
MP
N,�
LP
O
8.N
ame
two
angl
es t
hat
are
adj
acen
t.�
LP
M,�
MP
N o
r �
MP
N,�
NP
O�
NP
O,�
OP
L o
r �
OP
L,�
LP
M
Use
th
e fi
gure
at
the
righ
t to
nam
e th
e fo
llow
ing.
9.tw
o ac
ute
an
gles
�D
CH
,�JB
D10
.tw
o st
raig
ht
angl
es�
AB
D,�
EB
G11
.tw
o ri
ght
angl
es�
AB
E,�
GB
C12
.tw
o ob
tuse
an
gles
�F
GE
,�A
CH
FG
CB E
AD
H
J
P
LM
ON
6E
D
F7M
P
J3
H
GF
1C
BA
2X
Z
Y
4R
S
T
NA
ME
____
____
____
____
____
____
____
____
____
____
DA
TE
___
____
____
___
PE
RIO
D
____
_
Prac
tice
An
gle
Rel
atio
nsh
ips
Cha
pter
10
12G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-1
6MG
2.1
9–12
.Sam
ple
an
swer
s g
iven
.
Answers (Lesson 10-1)
Chapter 10 A3 Glencoe California Mathematics, Grade 6
NA
ME
____
____
____
____
____
____
____
____
____
____
DA
TE
___
____
____
___
PE
RIO
D
____
_
Cha
pter
10
15G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–2
pygp
10-2
Get
Rea
dy
for
the
Less
on
Com
ple
te t
he
Min
i L
ab a
t th
e to
p o
f p
age
514
in y
our
text
boo
k.
Wri
te y
our
answ
ers
bel
ow.
1.C
lass
ify
the
angl
e as
acu
te,r
igh
t,ob
tuse
,or
stra
igh
t.ri
gh
t
2.C
opy
the
angl
e on
to a
pie
ce o
f pa
per.
Th
en d
raw
a r
ay
that
cu
ts t
he
angl
e in
to t
wo
con
gru
ent
angl
es.L
abel
th
ese
two
con
gru
ent
angl
es �
1 an
d �
2.
3.W
hat
is
m�
1 an
d m
�2?
45°
4.W
hat
is
the
sum
of
m�
1 an
d m
�2?
90°
5.C
opy
the
orig
inal
an
gle
onto
a p
iece
of
pape
r.T
hen
dra
w
a
ray
that
sep
arat
es t
he
angl
e in
to t
wo
non
-con
gru
ent
angl
es.L
abel
th
ese
two
angl
es �
3 an
d �
4.
6.W
hat
is
tru
e ab
out
the
sum
of
m�
3 an
d m
�4?
T
hey
eq
ual
90°
.
7.C
ompl
ete
Exe
rcis
es 1
–6 f
or t
he
angl
e sh
own
at
the
righ
t.st
raig
ht;
See
dia
gra
m;T
hey
are
eac
h 9
0°.;
180°
;S
ee d
iag
ram
;Th
e su
m is
180
°.
Rea
d t
he
Less
on
Fil
l in
th
e b
lan
ks
to a
nsw
er Q
ues
tion
s 8
and
9.
8.T
wo
angl
es a
re c
ompl
emen
tary
if
the
sum
of
thei
r m
easu
re i
s .
9.T
wo
angl
es a
re s
upp
lem
enta
ry i
f th
e su
m o
f th
eir
mea
sure
is
.
Rem
emb
er W
hat
Yo
u L
earn
ed10
.55
°11
.13
5°
45°
x°35
° x°
180°
90°
43
21
34
12
6MG
2.1,
6M
G2.
2Le
sson
Rea
ding
Gui
deC
om
ple
men
tary
an
d S
up
ple
men
tary
An
gle
s
An
gle
s in
Bas
ebal
lA
ngl
es p
lay
an i
mp
orta
nt
par
t in
man
y sp
orts
.In
bas
ebal
l,in
fiel
der
sst
and
on
an
d c
over
dif
fere
nt
par
ts o
f th
e in
fiel
d d
epen
din
g on
th
ep
osit
ion
of
the
run
ner
s.S
omet
imes
,a p
laye
r w
ill
hav
e to
tu
rn v
aryi
ng
angl
es t
o m
ake
pla
ys.
For
Exe
rcis
es 1
an
d 2
,loo
k a
t th
ese
pic
ture
s of
bas
ebal
l fi
eld
s.In
eac
hon
e,th
e fo
ur
infi
eld
ers
cove
r d
iffe
ren
t ar
eas
of t
he
dia
mon
d.U
se a
pro
trac
tor
to d
eter
min
e th
e m
easu
re o
f th
e an
gle
of t
he
area
cov
ered
by
the
2nd
bas
eman
wit
h d
iffe
ren
t ru
nn
er p
osit
ion
s.
1.2.
43°
26°
3.T
he
outf
ield
is
cove
red
by t
hre
e ot
her
pla
yers
:th
e le
ft,c
ente
r,an
d ri
ght
outf
ield
ers.
Th
e ar
eas
they
cov
er m
ay o
verl
ap s
ligh
tly
depe
ndi
ng
onw
hoe
ver
is c
lose
st t
o th
e ba
ll;b
ut
in g
ener
al,
each
pla
yer
has
an
are
a to
cov
er.T
his
fig
ure
sh
ows
the
area
mos
t of
ten
cov
ered
by
each
ou
tfie
lder
.Wh
at t
ype
of a
ngl
e do
es e
ach
are
a m
ake
wit
h h
ome
plat
e? W
hat
typ
e of
an
gle
do
all
thre
e ou
tfie
ld a
reas
com
bin
ed c
reat
e w
ith
h
ome
plat
e?ac
ute
;ri
gh
t4.
Du
rin
g a
gam
e,th
e pi
tch
er n
otic
es t
he
run
ner
on
sec
ond
base
wan
ts t
o st
eal
thir
d ba
se.I
f th
e pi
tch
er i
s fa
cin
g h
ome
plat
e,w
hat
typ
e of
an
gle
does
th
e pi
tch
er h
ave
to t
urn
th
rou
gh t
o th
row
th
e ba
ll t
o th
ird
base
?ri
gh
t5.
Du
rin
g a
diff
eren
t in
nin
g,a
run
ner
is
on f
irst
bas
e an
d ap
pear
s to
wan
tto
ste
al s
econ
d ba
se.W
hat
typ
e of
an
gle
does
th
e pi
tch
er n
eed
to t
urn
thro
ugh
to
thro
w t
he
ball
to
seco
nd
base
if
the
pitc
her
is
faci
ng
hom
epl
ate?
stra
igh
t
Hom
ePl
ate
Third
Base
Seco
ndBa
seAr
ea c
over
edby
righ
t fie
lder
Area
cov
ered
by c
ente
r fie
lder
Area
cov
ered
by le
ft fie
lder
Firs
tBa
se
Hom
ePl
ate
Third
Base
Seco
ndBa
seAr
ea c
over
ed b
y th
ese
cond
bas
eman
Firs
tBa
se
Hom
ePl
ate
Third
Base
Seco
ndBa
seAr
ea c
over
ed b
y th
ese
cond
bas
eman
Firs
tBa
se
NA
ME
____
____
____
____
____
____
____
____
____
____
DA
TE
___
____
____
___
PE
RIO
D
____
_
Enri
chm
ent
Cha
pter
10
14G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-1
6MG
2.1
Answers (Lessons 10-1 and 10-2)
Chapter 10 A4 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DA
TE
___
____
____
___
PE
RIO
D
____
_
Cha
pter
10
17G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–2
10-2
Fin
d t
he
mis
sin
g an
gle
mea
sure
.
1.53
°2.
48°
3.65
°
4.48
°5.
95°
6.17
0°
7.70
°8.
94°
9.66
°
Use
th
e fi
gure
at
the
righ
t to
an
swer
Qu
esti
ons
10–1
3.
10.
Fin
d m
�H
JL
.15
0°
11.
�H
JL
and
�L
JM
are
wh
at t
ype
of a
ngl
es?
sup
ple
men
tary
12.
Fin
d m
�K
JM
.90
°
13.
�K
JL
and
�L
JM
are
wh
at t
ype
of a
ngl
es?
com
ple
men
tary
K JH
M
L
90°
30°
60°
24°
x°
43° 43
° x°
45°
65°
x°
10°
x°
85°
x°42
°
x°
25˚ x ˚
42˚
x ˚12
7˚
x˚
6MG
2.1,
6M
G2.
2Sk
ills
Prac
tice
Co
mp
lem
enta
ry a
nd
Su
pp
lem
enta
ry A
ng
les
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
10
16G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-2
Fin
d t
he
valu
e of
x.
Th
e tw
o an
gles
for
m a
rig
ht
angl
e or
90°
,so
they
are
com
plem
enta
ry,
Writ
e th
e eq
uatio
n.S
ubtr
act
43 f
rom
eac
h si
de.
so t
he
valu
e of
xis
47°
.
Fin
d t
he
valu
e of
x.
Th
e tw
o an
gles
for
m a
str
aigh
t li
ne
or 1
80°,
so t
hey
are
su
pple
men
tary
,
Writ
e th
e eq
uatio
n.S
ubtr
act
110
from
eac
h si
de.
so t
he
valu
e of
xis
70°
.
Fin
d t
he
valu
e of
xin
eac
h f
igu
re.
1.32
°2.
124°
3.95
°
4.19
°5.
45°
6.98
°
82°
x°45
°x°
71°
x°
85°
x°56
° x°
58°
x°
110
�x
�18
0�
110
�11
0x
�70
110˚
x
˚
43 �
x�
90�
43�
43x
�47
43° x°
•Tw
o an
gles
are
co
mp
lem
enta
ryif
the
sum
of
thei
r m
easu
re is
90°
.
m�
1 �
m�
2 �
90°
•Tw
o an
gles
are
su
pp
lem
enta
ryif
the
sum
of
thei
r m
easu
re is
180
°.
m�
3 �
m�
4 �
180°
•To
fin
d a
mis
sin
g a
ng
le m
easu
re,f
irst
dete
rmin
e if
the
angl
es a
re c
ompl
emen
tary
or
supp
lem
enta
ry.T
hen
writ
e an
equ
atio
n an
d su
btra
ct t
o fin
d th
e m
issi
ng m
easu
re.
34
12
Exam
ple
1
Exam
ple
2
Exer
cise
s
6MG
2.1,
6M
G2.
2St
udy
Guid
e an
d In
terv
entio
nC
om
ple
men
tary
an
d S
up
ple
men
tary
An
gle
s
Answers (Lesson 10-2)
Chapter 10 A5 Glencoe California Mathematics, Grade 6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
10
19G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–2
pygp
10-2
1.SI
GN
Th
e su
ppor
t w
ire
for
a si
gn
mee
ts t
he
wal
l an
d th
e ov
erh
ang
assh
own
bel
ow.I
f m
�2
�42
°,fi
nd
m�
1.E
xpla
in y
our
reas
onin
g
m�
1 �
48°;
�1
and
�2
are
com
ple
men
tary
an
gle
s.
21
2.ST
REE
TSM
ain
Str
eet
inte
rsec
ts
Oak
Roa
d.If
a r
igh
t-h
and
turn
on
toO
ak R
oad
requ
ires
a 7
7°tu
rn,w
hat
degr
ee m
ust
a l
eft-
han
d tu
rn o
nto
O
ak R
oad
mak
e?
A le
ft h
and
tu
rn r
equ
ires
a
103°
turn
.
77˚Oa
k Ro
ad
Mai
n St
reet
3.R
AIL
RO
AD
Eas
t of
th
e to
wn
of
Roc
kpor
t,th
e ra
ilroa
d tr
acks
inte
rsec
t H
ighw
ay 6
7as
sh
own
bel
ow.I
f m
�1
�13
3°,f
ind
m�
2.E
xpla
in y
our
reas
onin
g.
m�
2 �
47°;
�1
and
�2
are
sup
ple
men
tary
an
gle
s.
1 2
4.C
AM
PIN
GJo
nn
a an
d E
liza
beth
fou
nd
ale
vel
cam
psit
e an
d pi
tch
ed t
hei
r te
nt
assh
own
bel
ow.I
f m
�1
�12
0°,f
ind
m�
2.E
xpla
in y
our
reas
onin
g.
m�
2 �
60°;
�1
and
�2
are
sup
ple
men
tary
an
gle
s.
21
5.G
AS
GA
UG
EB
elow
is
a pi
ctu
re o
f th
e ga
s ga
uge
in
Ser
gio'
s ca
r.T
he
angl
es m
ade
by t
he
indi
cato
r ar
eco
mpl
emen
tary
.If
the
m�
1 �
42°,
wh
at i
s th
e m
�2?
48°
FU
EL
EF
12
6.A
RC
HIT
ECTU
RE
Th
e pl
ans
for
a n
ewaq
uar
ium
cal
l fo
r se
vera
l h
allw
ays
ofex
hib
its
lead
ing
out
of a
cir
cula
r m
ain
room
.Bec
ause
of
the
size
of
the
tan
ksth
at w
ill
be u
sed,
the
angl
e fo
rmed
betw
een
tw
o ad
jace
nt
hal
lway
s ca
n b
en
o sm
alle
r th
an 6
5°.W
hat
is
the
max
imu
m n
um
ber
of h
allw
ays
that
can
be b
uil
t le
adin
g ou
t of
th
e m
ain
roo
m?
5
Mai
n
R
oom
Hallw
ay
Hallw
ay
65˚
6MG
2.1,
6M
G2.
2W
ord
Prob
lem
Pra
ctic
eC
om
ple
men
tary
an
d S
up
ple
men
tary
An
gle
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
10
18G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-2
Fin
d t
he
valu
e of
xin
eac
h f
igu
re.
1.68
°2.
115°
3.47
°
4.15
1°5.
70°
6.10
8°
Cla
ssif
y ea
ch p
air
of a
ngl
es a
s co
mp
lem
enta
ry,s
up
ple
men
tary
,or
nei
ther
.
7.8.
9.
com
ple
men
tary
nei
ther
sup
ple
men
tary
ALG
EBR
AF
ind
th
e va
lue
of x
in e
ach
fig
ure
.
10.
11.
12.
40.9
9.5
160.
8
13.
ALG
EBR
AIf
�C
and
�D
are
supp
lem
enta
ry,a
nd
the
mea
sure
of
�D
is 4
5°,w
hat
is
the
mea
sure
of
�C
?13
5°
19.2
˚x˚
92˚
78.5
˚
x˚
49.1
˚ x˚
12
12
12
72°
x°11
0°
x°29
°
x°
43°
x°65
°x°
22° x°
6MG
2.1,
6M
G2.
2Pr
actic
eC
om
ple
men
tary
an
d S
up
ple
men
tary
An
gle
s
Answers (Lesson 10-2)
Chapter 10 A6 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
10
21G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–3
pygp
10-3
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n a
t th
e to
p o
f p
age
518
in y
our
text
boo
k.
Wri
te y
our
answ
ers
bel
ow.
1.E
xpla
in h
ow y
ou k
now
th
at e
ach
per
son
su
rvey
ed c
hos
e on
ly o
ne
shad
e of
blu
e.S
amp
le a
nsw
er:T
he
per
cen
ts a
dd
up
to
100
.
2.If
500
peo
ple
took
par
t in
th
e su
rvey
,how
man
y pr
efer
red
aqu
amar
ine?
85
Rea
d t
he
Less
on
3.In
th
e fo
llow
ing
circ
le g
raph
,wh
at i
s th
e pe
rcen
t re
pres
ente
d by
sect
ion
C?
How
do
you
kn
ow?
62.5
%;T
he
per
cen
ts m
ust
ad
d u
p t
o 1
00.
4.A
s st
ated
in
Exa
mpl
e 2
on p
age
519,
wh
en y
ou c
onst
ruct
a c
ircl
e gr
aph
,yo
u c
an c
hec
k yo
ur
wor
k by
mea
suri
ng
the
last
sec
tion
of
a ci
rcle
gra
ph
to v
erif
y th
at t
he
angl
es h
ave
the
corr
ect
mea
sure
s.W
hy
wil
l th
is w
ork
as a
ch
eck?
Sam
ple
an
swer
:If
th
e g
rap
h is
acc
ura
te t
hen
th
ela
st s
ecti
on
will
hav
e a
mea
sure
men
t co
rres
po
nd
ing
to
th
ep
erce
nt
rem
ain
ing
to
be
gra
ph
ed o
n t
he
circ
le.
Rem
emb
er W
hat
Yo
u L
earn
ed5.
If y
ou a
re g
iven
th
e re
sult
s of
a s
urv
ey a
nd
the
resu
lts
are
give
n i
npe
rcen
ts,h
ow d
o yo
u d
raw
a c
ircl
e gr
aph
to
repr
esen
t th
e re
sult
s of
th
esu
rvey
? D
escr
ibe
each
ste
p.S
amp
le a
nsw
er:
a.F
ind
th
e d
egre
es f
or
each
par
t.b
.Use
a c
om
pas
s to
dra
w a
cir
cle.
Th
en d
raw
a r
adiu
s.c.
Use
a p
rotr
acto
r to
dra
w t
he
ang
le t
hat
co
rres
po
nd
s to
eac
h p
erce
nt.
d.L
abel
eac
h s
ecti
on
of
the
gra
ph
.
Suc
cess
ful S
pac
eLa
unch
es, 2
001
12.5
%B C
25% A
5SD
AP
1.2
Less
on R
eadi
ng G
uide
Sta
tist
ics:
Dis
pla
y D
ata
in a
Cir
cle
Gra
ph
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
10
20G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-2
Mat
chst
ick
Puzz
les
Th
e p
uzz
les
on t
his
pag
e in
volv
e a
box
of
woo
den
mat
ches
.T
ooth
pic
ks
or a
ny
oth
er s
trai
ght
obje
cts
may
be
also
be
use
d.
Use
th
e sq
uar
e fi
gure
at
the
righ
t to
mak
e ea
ch o
f th
e fo
llow
ing
figu
res.
1.M
ove
3 m
atch
es t
o m
ake
2.M
ove
4 m
atch
es t
o m
ake
3 id
enti
cal
squ
ares
.3
iden
tica
l sq
uar
es.
3.R
emov
e 2
mat
ches
to
4.M
ove
2 m
atch
es t
o m
ake
mak
e 2
squ
ares
.7
squ
ares
.(Yo
u m
ay c
ross
th
e m
atch
es i
n t
his
on
e on
ly.)
Use
th
e h
exag
onal
fig
ure
at
the
righ
t to
mak
e ea
ch o
f th
e fo
llow
ing
firg
ure
s.
5.M
ove
4 m
atch
es t
o m
ake
6.M
ove
4 m
atch
es t
o m
ake
3 eq
uil
ater
al t
rian
gles
.4
iden
tica
l di
amon
ds.
Use
th
e sq
uar
e fi
gure
at
the
righ
t to
mak
e ea
ch o
f th
e fo
llow
ing
firg
ure
s.
5.R
emov
e 4
mat
ches
to
6.R
emov
e 6
mat
ches
to
mak
em
ake
5 id
enti
cal
squ
ares
.5
iden
tica
l sq
uar
es.
6MG
2.3
Answers (Lessons 10-2 and 10-3)
Chapter 10 A7 Glencoe California Mathematics, Grade 6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
10
23G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–3
pygp
10-3
For
eac
h t
able
,fin
d t
he
nu
mb
er o
f d
egre
es i
n e
ach
sec
tion
of
a ci
rcle
grap
h.T
hen
mak
e a
circ
le g
rap
h o
f th
e d
ata.
1.2.
Co
mm
erci
al a
nd
Ind
ust
rial
:18
7�M
om
:18
7�;
Dad
:61
�R
esid
enti
al:
72�
Bro
ther
/Sis
ter:
58�
Tran
spo
rtat
ion
:97
�;O
ther
:4�
Gra
nd
par
ent/
Oth
er:
54�
3.4.
Ind
ia:
22�;
Un
ited
Sta
tes:
251�
Atl
anti
c:61
�;P
acif
ic:
221�
Eu
rop
ean
Sp
ace
Ag
ency
:76
�G
ulf
:47
�C
hin
a:11
�A
rcti
c:32
�U
nite
d S
tate
s C
oas
tlin
e
17%
Atla
ntic
61%
Pac
ific
13%
Gul
fArc
tic9%
Suc
cess
ful S
pac
e La
unch
es, 2
001
21%
Eur
opea
nS
pac
eA
genc
y
70%
Uni
ted
Sta
tes
6% In
dia
3% C
hina
Fam
ily M
emb
ers
Stu
den
ts C
onf
ide
In
52%
Mom
17%
Dad
16%
Bro
ther
/S
iste
r
Gra
ndp
aren
t/O
ther
15%
Uni
ted
Sta
tes
Ene
rgy
Usa
ge,
200
1
52%
Com
mer
cial
and
Ind
ustr
ial
20%
Res
iden
tial
27%
Tran
spor
tatio
n
1% O
ther
Un
ited
Sta
tes
En
ergy
Usa
ge,2
001
Oth
er
Cat
egor
yP
erce
nt
Com
mer
cial
an
d In
dust
rial
52%
Res
iden
tial
20%
Tra
nsp
orta
tion
27% 1%
Fam
ily
Mem
ber
s S
tud
ents
Con
fid
e In
Gra
ndp
aren
t/O
ther
Fam
ily
Mem
ber
Per
cen
t
Mom
52%
Dad
17%
Bro
ther
/Sis
ter
16%
15%
Su
cces
sfu
l S
pac
e L
aun
ches
,200
1
Ch
ina
Cou
ntr
yN
um
ber
Indi
a2
Un
ited
Sta
tes
23
Eu
rope
an S
pace
Age
ncy
7 1
Un
ited
Sta
tes
Coa
stli
ne
Coa
stL
engt
h (
mil
es)
Atl
anti
c2,
100
Pac
ific
7,60
0
Gu
lf1,
600
Arc
tic
1,10
0
Un
ited
Sta
tes
Coa
stli
ne
Arc
tic
Coa
stL
engt
h (
mi)
Atl
anti
c2,
100
Pac
ific
7,60
0
Gu
lf1,
600
1,10
0
5SD
AP
1.2
Skill
s Pr
actic
eS
tati
stic
s:D
isp
lay
Dat
a in
a C
ircl
e G
rap
h
NA
ME
____
____
____
____
____
____
____
____
____
____
DA
TE
___
____
____
___
PE
RIO
D
____
_
Cha
pter
10
22G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-3
Exer
cise
s
ENER
GY
Mak
e a
circ
legr
aph
of
the
dat
a in
th
eta
ble
.St
ep 1
Fin
d th
e to
tal
nu
mbe
r of
rea
ctor
s:10
4 �
59 �
54 �
222
�43
9.St
ep 2
Fin
d th
e ra
tio
that
com
pare
s ea
chn
um
ber
wit
h t
he
tota
l.W
rite
th
era
tio
as a
dec
imal
rou
nde
d to
th
e n
eare
st h
un
dred
th.
Un
ited
Sta
tes:
�1 40 34 9��
0.24
Japa
n:
� 45 34 9��
0.12
Fra
nce
:� 45 39 9�
�0.
13O
ther
:�2 42 32 9�
�0.
51St
ep 3
Fin
d th
e n
um
ber
of d
egre
es f
or e
ach
sec
tion
of
the
grap
h.
Un
ited
Sta
tes:
0.24
· 36
0��
86�
Japa
n:
0.12
· 36
0��
43�
Fra
nce
:0.
13 ·
360�
�47
�O
ther
:0.
51 ·
360�
�18
4�St
ep 4
Use
a c
ompa
ss t
o co
nst
ruct
a c
ircl
e an
d dr
aw
a
radi
us.
Th
en u
se a
pro
trac
tor
to d
raw
an
86
°an
gle.
Th
is r
epre
sen
ts t
he
perc
ent
of
nu
clea
r re
acto
rs i
n t
he
Un
ited
Sta
tes.
Step
5F
rom
th
e n
ew r
adiu
s,dr
aw a
47°
angl
e fo
rF
ran
ce.R
epea
t th
is s
tep
for
the
oth
er t
wo
sect
ion
s.L
abel
eac
h s
ecti
on a
nd
give
th
e gr
aph
a t
itle
.
1.SW
IMM
ING
Th
e ta
ble
show
s th
e n
um
ber
of m
embe
rs o
f th
e sw
im t
eam
wh
o co
mpe
ted
at t
he
swim
mee
t.E
ach
com
pete
d in
on
ly o
ne
even
t.M
ake
a ci
rcle
gra
ph o
f th
e da
ta.
Nu
clea
r R
eact
ors
in O
per
atio
n, 2
001
24%
Uni
ted
Sta
tes
51%
Oth
erC
ount
ries
12%
Japa
n13%
Fra
nce
Agr
aph
that
sho
ws
data
as
part
s of
a w
hole
circ
le is
cal
led
a ci
rcle
gra
ph
.In
a c
ircle
gra
ph,
the
perc
ents
add
up
to 1
00.
Whe
n pe
rcen
ts a
re n
ot g
iven
, yo
u m
ust
first
det
erm
ine
wha
t pa
rt o
f th
e w
hole
each
item
rep
rese
nts.
Sw
im T
eam
Mem
ber
Par
tici
pat
ion
Bu
tter
fly
Eve
nt
Nu
mb
er
Fre
esty
le18
Bre
asts
trok
e7
Bac
kstr
oke
5 2
Sw
im T
eam
Mem
ber
Par
tici
pat
ion
56%
Free
styl
e
22%
Bre
asts
trok
e
6%B
utte
rfly
16%
Bac
kstr
oke
Exam
ple
1
Oth
er C
oun
trie
s
Un
ited
Sta
tes
104
Fra
nce
59
Japa
n54 222
Cou
ntr
yN
um
ber
of
Rea
ctor
s
Nu
clea
r R
eact
ors
in O
per
atio
n,2
001
5SD
AP
1.2
Stud
y Gu
ide
and
Inte
rven
tion
Sta
tist
ics:
Dis
pla
y D
ata
in a
Cir
cle
Gra
ph
Answers (Lesson 10-3)
Chapter 10 A8 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
10
25G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–3
pygp
10-3
LAN
GU
AG
ESF
or E
xerc
ises
1 a
nd
2,
use
th
e ta
ble
th
at s
how
s th
en
um
ber
of
peo
ple
th
at s
pea
k t
he
five
lan
guag
es t
hat
are
sp
oken
by
the
mos
t p
eop
le i
n t
he
wor
ld.
MIL
ITA
RYF
or E
xerc
ises
3 a
nd
4,u
se
the
tab
le t
hat
sh
ows
the
nu
mb
erof
peo
ple
act
ive
in t
he
Un
ited
Sta
tes
mil
itar
y in
200
2.
Cat
egor
yC
omm
erci
al a
nd
Indu
stri
alR
esid
enti
alT
ran
spor
tati
onO
ther
Spa
nis
hLan
guag
eS
pea
ker
s (m
illi
ons)
Hin
di36
6
En
glis
h34
1
322
Ben
gali
207
Ch
ines
e,M
anda
rin
874
Lan
guag
es S
pok
en b
y th
e M
ost
Peo
ple
1.F
ind
the
degr
ees
for
each
par
t of
aci
rcle
gra
ph t
hat
sh
ows
the
data
.C
hin
ese,
Man
dar
in:
150°
Hin
di:
62°
En
glis
h:
58°
Sp
anis
h:
55°
Ben
gal
i:35
°
2.M
ake
a ci
rcle
gra
ph o
f th
e da
ta.W
hic
hth
ree
lan
guag
es a
ccou
nt
for
41%
of
the
tota
l?
Ben
gal
i,S
pan
ish
,an
d
En
glis
h
Lang
uag
es S
po
ken
by
the
Mo
st P
eop
le
42%
Chi
nese
,M
and
arin
17%
Hin
di
16%
Eng
lish
15%
Sp
anis
h
Ben
gali
10%
Coa
st G
uar
d
Air
For
ceBra
nch
Per
son
nel
(th
ousa
nd
s)
Nav
y38
5
Mar
ine
Cor
ps17
4
368 38
Arm
y48
6
3.M
ake
a ci
rcle
gra
ph o
f th
e da
ta.
Uni
ted
Sta
tes
Mili
tary
Per
sonn
el A
ctiv
e D
uty,
200
2
33%
Arm
y
27%
Nav
yM
arin
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orp
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Forc
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uard
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4.W
hic
h t
wo
bran
ches
tak
en t
oget
her
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t fo
r al
mos
t h
alf
of t
he
tota
l?A
ir F
orc
e an
d N
avy
Un
ited
Sta
tes
Mil
itar
y,A
ctiv
e D
uty
,200
2
5SDAP1.2
Wor
d Pr
oble
m P
ract
ice
Sta
tist
ics:
Dis
pla
y D
ata
in a
Cir
cle
Gra
ph
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
10
24G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-3
Dis
pla
y ea
ch s
et o
f d
ata
in a
cir
cle
grap
h.
1.2.
EXPO
RTS
For
Exe
rcis
es 3
an
d 4
,use
th
e ci
rcle
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t of
Per
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year
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4.H
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5SD
AP
1.2
Prac
tice
Sta
tist
ics:
Dis
pla
y D
ata
in a
Cir
cle
Gra
ph
Answers (Lesson 10-3)
Chapter 10 A9 Glencoe California Mathematics, Grade 6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
TI-7
3 A
ctiv
ityC
ircl
e G
rap
hs
Cha
pter
10
27G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–3
pygp
10-3
Use
you
r ca
lcul
ator
to
mak
e ci
rcle
gra
phs
from
dat
a.
A g
roup
of
stud
ents
too
k a
surv
ey o
f fa
vori
te s
oft
drin
ks.M
ake
a ci
rcle
gra
ph
and
find
the
per
cent
of
each
fav
orit
e so
ft d
rink
.Her
e is
the
irda
ta t
able
.
Step
1E
nter
the
data
into
list
s. E
nter
the
cate
gory
dat
a in
L1
and
the
num
ber
data
in L
2. R
emem
ber
to u
se q
uote
sar
ound
the
firs
t ite
m in
the
cate
gory
dat
a. Y
ou c
anab
brev
iate
the
cate
gory
nam
es.
[MEM
]6
Mov
e ri
ght a
nd h
ighl
ight
the
firs
t bla
nk li
st.
Nam
e th
e ca
tego
ry D
RIN
K.
[TEX
T]"
D R
I N
K "
Don
e
[TEX
T]"
C O
L A
"D
one
Not
e:T
he le
tter
cap
pear
s in
L1,
bec
ause
it c
onta
ins
cate
gory
dat
a.Fi
ll in
the
rest
of
the
drin
k ca
tego
ries
. Ent
er th
e nu
mbe
r da
ta in
a li
st c
alle
d N
UM
BE
R.
Step
2S
et P
lot 1
. Fir
st tu
rn o
ff a
ll p
lots
.
[PLO
T]4
[PLO
T]1
Mak
e su
re D
rink
is th
e C
ateg
Lis
tand
Num
ber
is th
e D
ata
Lis
t. C
hoos
e N
umbe
r.
Step
3C
reat
e th
e ci
rcle
gra
ph. A
naly
ze th
e gr
aph.
Use
cur
sor
keys
wit
h .
Step
4C
reat
e a
circ
le g
raph
sho
win
g pe
rcen
ts.
Cho
ose
Perc
ento
n th
e P
lot 1
scr
een.
[PLO
T]1
In th
e ke
y sh
own
besi
de th
e gr
aph,
rea
d th
e pe
rcen
ts f
or e
ach
soft
dri
nk.
Ref
er t
o ci
rcle
gra
ph
you
cre
ate
d.
1,3.
See
stu
den
ts’w
ork
.
1.D
escr
ibe
the
circ
le g
raph
.
2.U
se t
he
perc
ent
circ
le g
raph
.Lis
t th
e pe
rcen
ts f
or e
ach
sof
t dr
ink.
cola
,33%
;D
C,1
1%;
RB
.31%
;L
L.1
5%;
oth
er,1
0%
3.W
hat
doe
s th
e ci
rcle
gra
ph t
ell
you
abo
ut
the
favo
rite
sof
t dr
inks
of
the
stu
den
tssu
rvey
ed?
Use
per
cen
ts i
n y
our
desc
ript
ion
.
GR
AP
HE
NT
ER
2nd
TR
AC
EG
RA
PH
TR
AC
E
EN
TE
R
EN
TE
RE
NT
ER
2nd
EN
TE
R2n
d
EN
TE
R2n
d
EN
TE
R2n
d
LIS
TE
NT
ER
2nd
Cat
egor
yN
umbe
r of
(Sof
t D
rink
)St
uden
ts
cola
28
diet
col
a (D
C)
9
root
bee
r (R
B)
26
lem
on-l
ime
(LL
)13
othe
r8
Exam
ple
Exer
cise
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
10
26G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
10-3
Enri
chm
ent
Rel
ativ
e Fr
equ
ency
an
d C
ircl
e G
rap
hs
Th
e re
lati
ve f
req
uen
cyte
lls
how
th
e fr
equ
ency
of o
ne
item
com
pare
s to
th
e to
tal
of a
ll t
he
freq
uen
cies
.Rel
ativ
e fr
equ
enci
es a
re w
ritt
en a
sfr
acti
ons,
deci
mal
s,or
per
cen
ts.
For
exa
mpl
e,in
Exe
rcis
e 1
belo
w,t
he
tota
l of
all
the
freq
uen
cies
is
50.S
o,th
e re
lati
ve f
requ
ency
of
the
grad
e A
is
8�
50,o
r 0.
16.
Th
e ci
rcle
at
the
righ
t is
div
ided
in
to 2
0 eq
ual
part
s.Yo
u c
an t
race
th
is c
ircl
e an
d th
en u
sere
lati
ve f
requ
enci
es t
o m
ake
circ
le g
raph
s.
Com
ple
te e
ach
ch
art
to s
how
th
e re
lati
vefr
equ
enci
es.T
hen
sk
etch
a c
ircl
e gr
aph
for
the
dat
a.U
se d
ecim
als
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nd
ed t
o th
e n
eare
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un
dre
dth
.
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ents
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0.36
Fre
qu
ency
8 16
Gra
de
18
A
6
B
Rel
ativ
eF
req
uen
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C D
0.16
0.32
0.36
0.12
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5SD
AP
1.2
Answers (Lesson 10-3)
Chapter 10 A10 Glencoe California Mathematics, Grade 6
An
swer
s
Exer
cise
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Tria
ng
les
Cha
pter
10
29G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–4
pygp
10-4
Fin
d t
he
valu
e of
xin
�A
BC
.
x�
66 �
52 �
180
The
sum
of
the
mea
sure
s is
180
.x
�11
8 �
180
Sim
plify
.�
118
� 1
18S
ubtr
act
118
from
eac
h si
de.
x�
62T
he
mis
sin
g an
gle
is 6
2�.
Cla
ssif
y th
e tr
ian
gle
by
its
angl
es a
nd
by
its
sid
es.
Th
e tr
ian
gle
has
on
e ob
tuse
an
gle
and
two
side
s th
e sa
me
len
gth
.So,
it i
s an
obt
use
,iso
scel
es t
rian
gle.
Fin
d t
he
mis
sin
g m
easu
re i
n e
ach
tri
angl
e.T
hen
cla
ssif
y th
e tr
ian
gle
as a
cute
,rig
ht,
or o
btu
se.
1.2.
3.
23�;
acu
te47
�;ri
gh
t95
�;o
btu
se
Cla
ssif
y ea
ch t
rian
gle
by
its
angl
es a
nd
by
its
sid
es.
4.5.
6.
acu
te,s
cale
ne
rig
ht,
iso
scel
eso
btu
se,s
cale
ne
40˚ 11
0˚30
˚
60˚ 70
˚50
˚
45˚
40˚
x˚43
˚
x˚82
˚
˚x75
˚
Tria
ngle
s ca
n be
cla
ssifi
ed b
y th
e m
easu
res
of t
heir
angl
es.A
n ac
ute
tri
ang
leha
s th
ree
acut
e an
gles
.A
n o
btu
se t
rian
gle
has
one
obtu
se a
ngle
.A r
igh
t tr
ian
gle
has
one
right
ang
le.
Tria
ngle
s ca
n al
so b
e cl
assi
fied
by t
he le
ngth
s of
the
ir si
des.
Sid
es t
hat
are
the
sam
e le
ngth
are
con
gru
ent
seg
men
tsan
d ar
e of
ten
mar
ked
by t
ick
mar
ks.I
n a
scal
ene
tria
ng
le,
all s
ides
hav
edi
ffere
nt le
ngth
s.A
n is
osc
eles
tria
ngle
has
at
leas
t tw
o co
ngru
ent
side
s.A
n eq
uila
tera
l tri
ang
leha
sal
l thr
ee s
ides
con
grue
nt.
A t
rian
gle
is a
figu
re w
ith th
ree
side
s an
d th
ree
angl
es.T
he s
ymbo
l for
tria
ngle
is �
.The
sum
of t
he
mea
sure
s of
the
angl
es o
f a tr
iang
le is
180
�.Yo
u ca
n us
e th
is to
find
a m
issi
ng a
ngle
mea
sure
in a
tria
ngle
.
A
B
C
66˚
˚x52
˚
120˚
Exam
ple
1
Exam
ple
2
6MG
2.2,
6M
G2.
3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Less
on R
eadi
ng G
uide
Tr
ian
gle
s
Cha
pter
10
28G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-4
Get
Rea
dy
for
the
Less
on
Com
ple
te t
he
Min
i L
ab a
t th
e to
p o
f p
age
524
in y
our
text
boo
k.W
rite
you
r an
swer
s b
elow
.
1.W
hat
kin
d of
an
gle
is f
orm
ed w
her
e th
e th
ree
vert
ices
mee
t?st
raig
ht
ang
le
2.R
epea
t th
e ac
tivi
ty w
ith
an
oth
er t
rian
gle.
Mak
e a
con
ject
ure
abou
t th
esu
m o
f th
e m
easu
res
of t
he
angl
es o
f an
y tr
ian
gle.
Th
e su
m o
f th
ean
gle
mea
sure
s o
f a
tria
ng
le is
180
�.
Rea
d t
he
Less
on
3.H
ow c
an y
ou i
ndi
cate
th
at t
wo
side
s of
a t
rian
gle
are
con
gru
ent?
Sam
ple
an
swer
:U
se t
he
sam
e n
um
ber
of
tick
mar
ks o
n e
ach
of
the
con
gru
ent
sid
es.
4.W
rite
th
e fo
llow
ing
equ
atio
n i
n w
ords
:m�
1 �
m�
2 �
m�
3 �
180�
.T
he
mea
sure
of
ang
le 1
plu
s th
e m
easu
re o
f an
gle
2 p
lus
the
mea
sure
of
ang
le 3
eq
ual
s 18
0 d
egre
es.
5.If
you
kn
ow t
he
mea
sure
s of
tw
o an
gles
of
a tr
ian
gle,
how
can
you
fin
dth
e m
easu
re o
f th
e th
ird
angl
e?S
amp
le a
nsw
er:
Set
up
an
equ
atio
n t
o f
ind
th
e m
easu
re o
f th
e th
ird
an
gle
usi
ng
th
e fa
ctth
at t
he
sum
of
all t
hre
e an
gle
s is
eq
ual
to
180
�.
Rem
emb
er W
hat
Yo
u L
earn
ed6.
Com
plet
e th
e ta
ble
to h
elp
you
rem
embe
r th
e w
ays
to c
lass
ify
tria
ngl
es.
Cla
ssif
ied
by
A
ngl
es o
r S
ides
angl
es
ang
les
Typ
e of
Tri
angl
e
side
s
acu
te
ang
les
obtu
se
Des
crip
tion
scal
ene
rig
ht
all a
cute
an
gle
s
1 o
btu
se a
ng
le
no
con
gru
ent
side
s
1 ri
ght
angl
e
sid
esis
osce
les
at le
ast
2 co
ng
ruen
t si
des
sid
eseq
uil
ater
al3
con
gru
ent
sid
es
6MG
2.2,
6M
G2.
3
Answers (Lesson 10-4)
Chapter 10 A11 Glencoe California Mathematics, Grade 6
Fin
d t
he
valu
e of
x.
1.2.
3.
4.5.
6.
Fin
d t
he
mis
sin
g m
easu
re i
n e
ach
tri
angl
e w
ith
th
e gi
ven
an
gle
mea
sure
s.
7.45
°,35
.8°,
x°99
.28.
100°
,x°,
40.7
°39
.39.
x°,9
0°,1
6.5°
73.5
10.
Fin
d th
e th
ird
angl
e of
a r
igh
t tr
ian
gle
if o
ne
of t
he
angl
es m
easu
res
24°.
66°
11.
Wh
at i
s th
e th
ird
angl
e of
a r
igh
t tr
ian
gle
if o
ne
of t
he
angl
es m
easu
res
51.1
°?38
.9°
12.
ALG
EBR
AF
ind
m�
Ain
�A
BC
if m
�B
�38
°an
d m
�C
�38
°.10
4°
13.
ALG
EBR
AIn
�X
YZ
,m�
Z�
113°
and
m�
X�
28°.
Wh
at i
s m
�Y
?39
°
Cla
ssif
y th
e m
ark
ed t
rian
gle
in e
ach
ob
ject
by
its
angl
es a
nd
by
its
sid
es.
14.
15.
16.
ALG
EBR
AF
ind
th
e va
lue
of x
in e
ach
tri
angl
e.
20.
3621
.22
.
2x˚
x˚
x˚7x
˚
3x˚
2x˚
2x˚
x˚
30˚
30˚
40˚
50˚
25˚
60˚
60˚̊
x˚
41˚
37˚
x˚29
˚
61˚̊ x˚
17˚
x˚
22˚
140˚
x˚
42˚
x˚
NA
ME
____
____
____
____
____
____
____
____
____
____
DA
TE
___
____
____
___
PE
RIO
D
____
_
Prac
tice
Tria
ng
les
Cha
pter
10
31G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–4
pygp
10-4
73
acu
te;
iso
scel
es
ob
tuse
;is
osc
eles
rig
ht;
scal
ene
48 90
18
102
60
9456M
G2.
2, 6
MG
2.3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Skill
s Pr
actic
eTr
ian
gle
s
Cha
pter
10
30G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-4
Fin
d t
he
mis
sin
g m
easu
re i
n e
ach
tri
angl
e.T
hen
cla
ssif
y th
e tr
ian
gle
as a
cute
,rig
ht,
or o
btu
se.
1.2.
3.
15�;
acu
te12
0�;
ob
tuse
41�;
rig
ht
4.5.
6.
104�
;o
btu
se25
�;ri
gh
t64
�;ac
ute
7.8.
9.
72�;
acu
te32
�;o
btu
se40
�;ri
gh
tC
lass
ify
each
tri
angl
e b
y it
s an
gles
an
d b
y it
s si
des
.
10.
11.
12.
acu
te,i
sosc
eles
ob
tuse
,iso
scel
esri
gh
t,sc
alen
e13
.14
.15
.
acu
te,e
qu
ilate
ral
rig
ht,
iso
scel
eso
btu
se,s
cale
ne
16.
17.
18.
ob
tuse
,iso
scel
esac
ute
,sca
len
eac
ute
,iso
scel
es
27˚
46˚
82˚
52˚
98˚
121˚
40˚
19˚
60˚
60˚
60˚
50˚
40˚
114˚
37˚
50˚
x˚
126˚
22˚
x˚51
˚
57˚
x˚
71˚
45˚
x˚
65˚
x˚38
˚
38˚x˚
49˚
x˚24
˚
36˚
x˚
81˚
84˚
x˚
6MG
2.2,
6M
G2.
3
Answers (Lesson 10-4)
Chapter 10 A12 Glencoe California Mathematics, Grade 6
An
swer
s
Tria
ng
le S
um
sT
he
mea
sure
s of
th
e an
gles
of
a tr
ian
gle
alw
ays
add
up
to 1
80°.
Th
esi
des
of a
tri
angl
e al
so h
ave
a sp
ecia
l re
lati
onsh
ip.I
n t
his
act
ivit
y,yo
u w
ill
expl
ore
the
rela
tion
ship
s of
th
e si
de l
engt
hs.
Cu
t th
e st
rips
of
pape
r fr
om t
he
righ
t si
de o
f th
is p
age.
Use
th
e 3
spec
ifie
d st
rips
for
eac
h p
robl
em.T
ell
if a
tri
angl
e ca
n b
e fo
rmed
wit
h t
hem
.If
so,t
ell
wh
at t
ype
of t
rian
gle
it i
s.1.
6 cm
,14
cm,a
nd
14 c
m
2.6
cm,6
cm
,14
cm
iso
scel
es t
rian
gle
no
t a
tria
ng
le
3.6
cm,8
cm
,14
cm4.
3 cm
,3 c
m,6
cm
no
t a
tria
ng
len
ot
a tr
ian
gle
5.3
cm,6
cm
,8 c
m6.
6 cm
,6 c
m,8
cm
scal
ene
tria
ng
leis
osc
eles
tri
ang
le
7.L
ook
at y
our
answ
ers
abov
e.C
hoo
se a
ny
set
of s
ide
len
gth
s th
at f
orm
atr
ian
gle.
Add
th
e tw
o sh
orte
st m
easu
res.
Com
pare
th
at s
um
wit
h t
he
lon
gest
sid
e le
ngt
h.T
ry t
his
wit
h a
ll t
he
tria
ngl
es a
bove
.Wh
at c
oncl
usi
onca
n y
ou m
ake
abou
t tr
ian
gle
side
len
gth
s?T
he
sum
of
the
len
gth
so
f an
y tw
o s
ides
of
a tr
ian
gle
is g
reat
er t
han
th
e le
ng
th o
fth
e th
ird
sid
e.
8.N
ow l
ook
at t
he
sets
of
side
len
gth
s th
at d
id n
ot f
orm
tri
angl
es.A
dd t
he
two
shor
test
sid
es.C
ompa
re t
he
sum
wit
h t
he
len
gth
of
the
thir
d si
de.
Wh
at c
oncl
usi
on c
an y
ou m
ake
abou
t th
ree
len
gth
s th
at d
o n
ot m
ake
atr
ian
gle?
Th
e su
m o
f th
e le
ng
ths
of
the
two
sh
ort
est
sid
es is
less
th
an o
r eq
ual
to
th
e le
ng
th o
f th
e lo
ng
est
sid
e.
9.W
hat
ru
le c
an y
ou g
ive
to t
est
any
thre
e se
gmen
t le
ngt
hs
to f
ind
out
ifth
e se
gmen
ts w
ill
form
a t
rian
gle?
Th
e su
m o
f th
e le
ng
ths
of
the
two
sh
ort
est
sid
es m
ust
be
gre
ater
th
an t
he
len
gth
of
the
thir
d s
ide.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
10
33G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–4
pygp
10-4
6MG
2.2,
6M
G2.
3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Wor
d Pr
oble
m P
ract
ice
Tria
ng
les
Cha
pter
10
32G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-4
1.TA
ILO
RIN
GE
ach
lap
el o
n a
su
it ja
cket
is
in t
he
shap
e of
a t
rian
gle.
Th
e th
ree
angl
es o
f ea
ch t
rian
gle
mea
sure
47�
,68
�,an
d 65
�.C
lass
ify
the
tria
ngl
e by
its
angl
es.
acu
te
2.FL
AG
SA
nav
al d
istr
ess
sign
al f
lag
is i
nth
e sh
ape
of a
tri
angl
e.T
he
thre
e si
des
of t
he
tria
ngl
e m
easu
re 5
fee
t,9
feet
,an
d 9
feet
.Cla
ssif
y th
e tr
ian
gle
by i
tssi
des.
iso
scel
es
3.C
AR
PEN
TRY
Th
e su
ppor
ts o
f a
woo
dta
ble
are
in t
he
shap
e of
a r
igh
ttr
ian
gle.
Fin
d th
e th
ird
angl
e of
th
etr
ian
gle
if t
he
mea
sure
of
one
of t
he
angl
es i
s 23
�.67
�
4.M
APS
Th
e th
ree
tow
ns
of R
ipon
,S
part
a,an
d W
alke
r fo
rm a
tri
angl
e as
show
n b
elow
.Cla
ssif
y th
e tr
ian
gle
byit
s an
gles
an
d by
its
sid
es.W
hat
is
the
valu
e of
xin
th
e tr
ian
gle?
ob
tuse
,iso
scel
es;
38
38˚ 10
4˚˚x
Ripo
n
Spar
taW
alke
r
47 m
i30
mi
30 m
i
5.H
IKIN
GT
he
figu
re s
how
s th
e O
akC
reek
tra
il,w
hic
h i
s sh
aped
lik
e a
tria
ngl
e.C
lass
ify
the
tria
ngl
e by
its
angl
es a
nd
by i
ts s
ides
.W
hat
is
the
valu
e of
xin
th
e fi
gure
?
acu
te,s
cale
ne;
41
61˚
78˚
˚x
Rock
y Pe
ak
Mea
dow
Trai
l Hea
d
1.2
mi
0.8
mi
1.1
mi
Oak
Cree
k
6.LA
DD
ERT
he
figu
re s
how
s a
ladd
erle
anin
g ag
ain
st a
wal
l,fo
rmin
g a
tria
ngl
e.C
lass
ify
the
tria
ngl
e by
its
angl
es a
nd
by i
ts s
ides
.Wh
at i
s th
eva
lue
of x
in t
he
figu
re?
rig
ht,
scal
ene;
2466˚
˚x9
ft
4 ft
6MG
2.2,
6M
G2.
3
Answers (Lesson 10-4)
Chapter 10 A13 Glencoe California Mathematics, Grade 6
Use
log
ical
rea
son
ing
to s
olve
.
1.G
EOM
ETRY
Dra
w s
ever
al s
quar
es a
nd m
easu
re t
heir
int
erio
r an
gles
.Wha
tca
n yo
u co
nclu
de a
bout
the
mea
sure
s of
the
ang
les
of a
squ
are?
Did
you
use
indu
ctiv
e or
ded
ucti
ve r
easo
ning
?T
hey
are
eac
h 9
0°;i
nd
uct
ive.
2.M
ON
EYL
uke
is
inve
stin
g m
oney
in
a s
avin
gs a
ccou
nt.
Use
th
e fo
rmu
la
I�
Prt
wh
ere
Iis
th
e am
oun
t of
in
tere
st e
arn
ed,P
is t
he
prin
cipa
lam
oun
t of
mon
ey i
nve
sted
,ris
th
e in
tere
st r
ate,
and
tis
th
e le
ngt
h o
fti
me
the
mon
ey i
s in
vest
ed.I
f L
uke
in
vest
s 50
0 at
5%
in
tere
st f
or 1
yea
r,h
ow m
uch
in
tere
st w
ill
he
earn
? D
id y
ou u
se i
ndu
ctiv
e or
ded
uct
ive
reas
onin
g? $2
5;d
edu
ctiv
e
3.PA
TTER
NS
Wri
te a
ru
le t
o re
pres
ent
the
patt
ern
sh
own
bel
ow.D
id y
ou u
sein
duct
ive
or d
edu
ctiv
e re
ason
ing?
2,
4,6,
8,10
,…2n
;in
du
ctiv
e
4.ST
UD
ENT
CO
UN
CIL
Ch
en,S
ue
and
Jaco
b ar
e pr
esid
ent,
vice
pre
side
nt
and
secr
etar
y of
th
e st
ude
nt
cou
nci
l,n
ot n
eces
sari
ly i
n t
hat
ord
er.C
hen
an
dth
e vi
ce p
resi
den
t st
ayed
aft
er s
choo
l w
ith
Jac
ob t
o pl
an a
dan
ce.C
hen
is
not
th
e pr
esid
ent.
Wh
o is
th
e pr
esid
ent?
Jaco
b
5.G
EOM
ETRY
Dra
w s
ever
al p
aral
lelo
gram
s an
d m
easu
re t
hei
r si
des.
Wh
atca
n y
ou c
oncl
ude
abo
ut
the
mea
sure
s of
th
e op
posi
te s
ides
of
apa
rall
elog
ram
? D
id y
ou u
se i
ndu
ctiv
e or
ded
uct
ive
reas
onin
g?T
hey
are
co
ng
ruen
t;in
du
ctiv
e.
6.TR
AV
ELU
se t
he
form
ula
D�
rtw
her
e D
is t
he
dist
ance
,ris
th
e ra
te,a
nd
tis
th
e ti
me
to d
eter
min
e h
ow f
ar L
uci
nda
tra
vele
d if
sh
e dr
ove
65 m
iles
per
hou
r fo
r 6
hou
rs w
ith
out
stop
pin
g.D
id y
ou u
se i
ndu
ctiv
e or
ded
uct
ive
reas
onin
g?39
0 m
iles;
ded
uct
ive
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
10
35G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–5
pygp
10-5
6MR
1.2,
6M
G2.
3Sk
ills
Prac
tice
Pro
blem
-So
lvin
g In
vest
igat
ion
:Use
Lo
gic
al R
easo
nin
g
Exam
ple
Use
th
e fo
rmu
la d
�rt
wh
ere
dis
dis
tan
ce,r
is r
ate,
and
tis
ti
me
to d
eter
min
e h
ow f
ar a
car
has
tra
vele
d a
fter
4 h
ours
if
it i
s tr
avel
ing
at a
rat
e of
65
mp
h.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
10
34G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-5
Logi
cal r
easo
ning
is a
met
hod
of p
robl
em s
olvi
ng t
hat
uses
ind
uct
ive
reas
on
ing
,mak
ing
a ru
le a
fter
seei
ng s
ever
al e
xam
ples
or
ded
uct
ing
rea
son
ing
,use
a r
ule
to m
ake
a de
cisi
on.
Exp
lore
You
kn
ow t
he
car
has
tra
vele
d fo
r 4
hou
rs a
t 65
mph
.P
lan
Try
a f
ew e
xam
ples
to
fin
d a
patt
ern
.M
ake
a ta
ble.
Sol
ve
Aft
er e
ach
hou
r th
e ca
r h
as t
rave
led
65 m
ore
mil
es.
So
afte
r 4
hou
rs t
he
car
wil
l h
ave
trav
eled
260
mil
es.
Exa
min
eT
he
form
ula
is
d �
rtso
d�
65 �
4 or
260
mi.
Hou
rs P
asse
dD
ista
nce
Tra
vele
d(i
n m
iles
)1
651.
597
.52
130
2.5
162.
53
195
t65
t
Sol
ve t
he
foll
owin
g p
rob
lem
s u
sin
g lo
gica
l re
ason
ing.
1.TR
AV
ELU
se t
he
form
ula
d�
rtw
her
e d
is t
he
dist
ance
,ris
th
e ra
te,a
nd
tis
th
e ti
me
to d
eter
min
e h
ow f
ar t
he
Mor
alez
fam
ily
has
tra
vele
d if
th
eyar
e dr
ivin
g at
a r
ate
of 7
2 m
iles
per
hou
r fo
r 9
hou
rs.
648
mile
s
2.C
ELL
PHO
NES
Det
erm
ine
the
cost
per
ph
one
call
if
Mar
ia m
ade
30 c
alls
last
mon
th a
nd
her
tot
al b
ill
for
the
mon
th w
as $
45.0
0.$1
.50
per
cal
l
3.M
USI
CS
arah
,Ju
an,a
nd
Der
rick
pla
y th
e pi
ano,
tru
mpe
t,an
d vi
olin
,bu
tn
ot n
eces
sari
ly i
n t
hat
ord
er.
Sar
ah a
nd
Der
rick
sit
on
eit
her
sid
e of
th
etr
um
pet
play
er.S
arah
doe
s n
ot p
lay
the
viol
in.W
ho
play
s th
e vi
olin
?D
erri
ck
Exer
cise
s
6MR
1.2,
6M
G2.
3St
udy
Guid
e an
d In
terv
entio
nP
rob
lem
-So
lvin
g In
vest
igat
ion
:U
se L
og
ical
Rea
son
ing
Answers (Lesson 10-5)
Chapter 10 A14 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
10
37G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–5
pygp
10-5
1.PH
YSI
CS
A b
all
is d
ropp
ed f
rom
a h
eigh
tof
40
feet
.If
the
ball
bou
nce
s �1 2�
as h
igh
on e
ach
su
cces
sive
bou
nce
,wh
at i
s th
eh
eigh
t on
th
e fo
urt
h b
oun
ce?
2�1 2�
feet
2.R
ECIP
ESS
haw
n i
s m
akin
g a
cake
.He
nee
ds a
tot
al o
f 3�
1 4�cu
ps o
f fl
our.
If h
eh
as a
lrea
dy a
dded
2�1 2�
cups
,how
mu
chm
ore
does
he
nee
d to
add
?D
A2
cups
C�1 2�
cup
B1
cup
D�3 4�
cup
3.G
EOM
ETRY
Dra
w s
ever
al p
enta
gon
san
d m
easu
re t
hei
r in
teri
or a
ngl
es.
Wh
at c
an y
ou c
oncl
ude
abo
ut
the
sum
of t
he
mea
sure
s of
th
e an
gles
of
ape
nta
gon
? D
id y
ou u
se i
ndu
ctiv
e or
dedu
ctiv
e re
ason
ing?
540°
;in
du
ctiv
e
4.PA
TTER
NS
Fin
d th
e n
ext
thre
e te
rms
is t
he
sequ
ence
.2,
5,9,
14,…
20,2
7,35
5.W
OR
KT
he
tabl
e be
low
sh
ows
how
mu
ch L
u g
ot p
aid
base
d on
th
e n
um
ber
of h
ours
sh
e ba
bysa
t.P
redi
ct h
er p
ayfo
r 7
hou
rs.
$35
6.G
EOM
ETRY
Use
th
e fo
rmu
la V
�B
hw
her
e V
is t
he
volu
me
of a
cyl
inde
r,B
is t
he
area
of
the
base
an
d h
is t
he
hei
ght
of t
he
cyli
nde
r to
fin
d th
evo
lum
e of
th
e cy
lin
der
belo
w.
28 in
3
B =
3.5
in2
h =
8 in
7.FR
AM
ING
A p
hot
ogra
ph i
s 8
in.b
y 10
in
.an
d is
to
be s
urr
oun
ded
by a
mat
that
is
1.5
in.a
ll a
rou
nd.
Wh
at w
ill
beth
e di
men
sion
s of
th
e pi
ctu
re a
nd
mat
toge
ther
?11
in.b
y 13
in.
8.SC
HO
OL
Stu
den
ts f
ille
d ou
t a
surv
eyab
out
thei
r fa
vori
te s
choo
l su
bjec
ts.T
he
resu
lts
are
show
n i
n t
he
bar
grap
hbe
low
.How
man
y m
ore
stu
den
ts l
iste
dE
ngl
ish
as
thei
r fa
vori
te s
ubj
ect
than
mat
h?
10
Soci
alSt
udie
sM
ath
Engl
ish
Scie
nce
20 10 030 25 15 5
Nu
mb
er o
f h
ours
Pay
1$5
2$1
03
$15
4$2
0
6MR
1.2,
6M
G2.
3W
ord
Prob
lem
Pra
ctic
eP
robl
em-S
olv
ing
Inve
stig
atio
n:U
se L
og
ical
Rea
son
ing
Sele
ct t
he
Op
erat
ion
Mix
ed P
rob
lem
Sol
vin
g
For
Exe
rcis
es 1
an
d 2
,use
log
ical
reas
onin
g to
sol
ve t
he
pro
ble
m.
1.TO
WN
ST
ia,B
ian
ca,a
nd
Hir
oko
live
in
the
tow
ns
of P
arks
ide,
Wes
tlak
e,an
dS
um
mer
vill
e,bu
t n
ot n
eces
sari
ly i
n t
hat
orde
r.T
ia a
nd
her
fri
end
that
liv
es i
nW
estl
ake
hel
ped
Bia
nca
wit
h h
er c
hor
es.
Bia
nca
doe
s n
ot l
ive
in P
arks
ide.
Wh
ere
does
Tia
liv
e? D
id y
ou u
se i
ndu
ctiv
e or
dedu
ctiv
e re
ason
ing?
Par
ksid
e;d
edu
ctiv
e re
aso
nin
g
2.G
EOM
ETRY
Dra
w a
rig
ht
tria
ngl
e.M
ark
the
mid
poin
ts o
f ea
ch s
ide
of t
he
tria
ngl
e an
d dr
aw a
sm
alle
r tr
ian
gle
byco
nn
ecti
ng
the
mid
poin
ts.D
o th
isse
vera
l m
ore
tim
es.W
hat
can
you
con
clu
de a
bou
t th
e sm
alle
r tr
ian
gle?
D
id y
ou u
se i
ndu
ctiv
e or
ded
uct
ive
reas
onin
g?T
he
smal
ler
tria
ng
le
is a
rig
ht
tria
ng
le.;
ind
uct
ive
reas
on
ing
Use
an
y st
rate
gy t
o so
lve
Exe
rcis
es 3
and
4.S
ome
stra
tegi
es a
re s
how
n b
elow
.
3.A
NG
LES
On
e an
gle
of a
tri
angl
e is
33°
less
th
an t
he
oth
er t
wo
angl
es.F
ind
the
mea
sure
s of
th
e an
gles
of
the
tria
ngl
e.D
id y
ou u
se i
ndu
ctiv
e or
ded
uct
ive
reas
onin
g?38
°,71
°,71
°;d
edu
ctiv
e re
aso
nin
g
4.M
ETEO
RIT
ESA
n a
stro
nom
er f
oun
d th
ree
met
eori
tes
wei
ghin
g 9.
4 po
un
ds,5
.7po
un
ds,a
nd
24.5
pou
nds
.If
1 ki
logr
amw
eigh
s 2.
2 po
un
ds,f
ind
the
aver
age
mas
s of
th
e m
eteo
rite
s in
kil
ogra
ms.
6 kg
For
Exe
rcis
es 5
an
d 6
,sel
ect
the
app
rop
riat
e op
erat
ion
(s)
to s
olve
th
ep
rob
lem
s.J
ust
ify
you
r se
lect
ion
s an
dso
lve
the
pro
ble
m.
5.PU
BLI
C T
RA
NSP
OR
TATI
ON
A b
us
stop
ped
at a
bu
s st
op a
nd
12 p
eopl
e go
t on
an
d 5
got
off.
At
the
nex
t st
op,1
4 pe
ople
got
on a
nd
3 go
t of
f.If
th
e n
um
ber
ofpa
ssen
gers
has
dou
bled
,fin
d th
en
um
ber
of p
asse
nge
rs o
n t
he
bus.
Su
btr
acti
on
,ad
dit
ion
an
dm
ult
iplic
atio
n;
12 �
5 �
7,14
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;7
�11
�18
;18
�2
�36
6.D
ISC
OU
NTS
Th
e ta
ble
show
s th
edi
ffer
ent
disc
oun
ts t
wo
stor
es o
ffer
for
the
sam
e pr
odu
ct.W
hic
h s
tore
off
ers
the
bett
er p
rice
aft
er t
he
disc
oun
t is
app
lied
and
by h
ow m
uch
?
Su
btr
acti
on
an
d m
ult
iplic
atio
n;
0.25
�13
9 �
34.7
5;13
9.00
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104.
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0.25
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tore
A;
$0.2
5
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
10
36G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-5 P
RO
BL
EM
-SO
LVIN
G S
TR
AT
EG
IES
•U
se t
he fo
ur-s
tep
plan
.
•Lo
ok fo
r a
patte
rn.
•U
se a
gra
ph.
•U
se lo
gica
l rea
soni
ng.
Pri
ceD
isco
un
tS
tore
A$1
29.0
0$2
5S
tore
B$1
39.0
025
%
6MR
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G2.
3Pr
actic
eP
robl
em-S
olv
ing
Inve
stig
atio
n:U
se L
og
ical
Rea
son
ing
Answers (Lesson 10-5)
Chapter 10 A15 Glencoe California Mathematics, Grade 6
Exam
ple
Exer
cise
s
Qua
drila
tera
ls c
an b
e cl
assi
fied
usin
g th
eir
angl
es a
nd s
ides
.The
bes
t de
scrip
tion
of a
qua
drila
tera
l is
the
one
that
is t
he m
ost
spec
ific.
Exam
ple
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Qu
adri
late
rals
Cha
pter
10
39G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–6
pygp
10-6
Cla
ssif
y th
e q
uad
rila
tera
l u
sin
g th
e n
ame
that
bes
td
escr
ibes
it.
aT
he
quad
rila
tera
l is
a p
aral
lelo
gram
wit
h
4 co
ngr
uen
t si
des.
It i
s a
rhom
bus.
bT
he
quad
rila
tera
l h
as o
ne
pair
of
para
llel
sid
es.
It i
s a
trap
ezoi
d.
cT
he
quad
rila
tera
l is
a p
aral
lelo
gram
wit
h 4
rig
ht
angl
es.
It i
s a
rect
angl
e.
Fin
d t
he
mis
sin
g m
easu
re i
n t
he
qu
adri
late
ral.
100
�11
0�
60�
x�
360
Writ
e th
e eq
uatio
n.27
0�
x�
360
Sim
plify
.�
270
� 2
70S
ubtr
act
270
from
x
�90
each
sid
e.S
o,th
e m
issi
ng
mea
sure
is
90°.
Cla
ssif
y th
e q
uad
rila
tera
l u
sin
g th
e n
ame
that
bes
td
escr
ibes
it.
1.2.
3.
Fin
d t
he
mis
sin
g an
gle
mea
sure
in
eac
h q
uad
rila
tera
l.
4.5.
111�
6.
125˚
54˚
96˚
x˚95
˚
72˚
82˚
x˚13
5˚
88˚
45˚
x˚
100˚
110˚
60˚
x˚
Rec
tan
gle
para
llelo
gram
with
4 rig
ht a
ngle
s
Trap
ezo
id
one
pair
of p
aral
lel
side
s
Rh
om
bus
para
llelo
gram
with
4 co
ngru
ent
side
s
Sq
uar
e
para
llelo
gram
with
4 rig
ht a
ngle
s an
d4
cong
ruen
t si
des
Par
alle
log
ram
oppo
site
sid
es
para
llel a
nd
oppo
site
sid
es
cong
ruen
t
qu
adri
late
ral
rho
mbu
sp
aral
lelo
gra
m
85°
92�
6MG2.3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Less
on R
eadi
ng G
uide
Q
uad
rila
tera
ls
Cha
pter
10
38G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-6
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n a
t th
e to
p o
f p
age
533
in y
our
text
boo
k.
Wri
te y
our
answ
ers
bel
ow.
1.D
escr
ibe
the
angl
es i
nsi
de t
he
fou
r-si
ded
figu
re.
two
acu
te a
nd
tw
o o
btu
se a
ng
les
2.W
hic
h s
ides
of
the
figu
re a
ppea
r to
be
para
llel
?to
p a
nd
bo
tto
m
3.W
hic
h s
ides
app
ear
to b
e co
ngr
uen
t?le
ft a
nd
rig
ht
Rea
d t
he
Less
on
4.In
th
e di
agra
m o
f qu
adri
late
rals
on
pag
e 53
3,w
hat
do
the
arro
wh
eads
on
the
para
llel
ogra
m a
nd
trap
ezoi
d in
dica
te?
Op
po
site
sid
es a
re p
aral
lel.
5.W
hy
are
all
the
figu
res
on t
he
page
cal
led
quad
rila
tera
ls?
All
fig
ure
s h
ave
fou
r si
des
.
6.H
ow i
s a
trap
ezoi
d di
ffer
ent
from
a r
hom
bus,
a sq
uar
e,an
d a
rect
angl
e?S
amp
le a
nsw
er:
A t
rap
ezo
id h
as o
ne
pai
r o
f p
aral
lel s
ides
.Arh
om
bus,
a sq
uar
e,an
d a
rec
tan
gle
hav
e tw
o p
airs
of
par
alle
l sid
es.
7.In
th
e di
agra
ms
of t
he
para
llel
ogra
m,r
hom
bus,
squ
are,
and
rect
angl
e,h
ow d
o yo
u k
now
th
at c
erta
in s
ides
are
con
gru
ent?
Sam
ple
an
swer
:T
ick
mar
ks in
dic
ate
con
gru
ent
sid
es;
sin
gle
an
d d
ou
ble
tic
km
arks
ind
icat
e d
iffe
ren
t le
ng
ths
of
con
gru
ent
sid
es.
Rem
emb
er W
hat
Yo
u L
earn
ed8.
Wor
k w
ith
a p
artn
er.T
ake
turn
s dr
awin
g qu
adri
late
rals
.Hav
e th
e ot
her
pers
on g
ive
all
poss
ible
nam
es f
or t
he
quad
rila
tera
l.T
hen
dec
ide
on t
he
best
nam
e fo
r th
e qu
adri
late
ral.
For
exa
mpl
e,if
on
e pe
rson
dra
ws
asq
uar
e,th
e ot
her
per
son
sh
ould
say
th
at i
t is
a q
uad
rila
tera
l,a
para
llel
ogra
m,a
rec
tan
gle,
and
a rh
ombu
s,bu
t th
e be
st n
ame
for
the
figu
re i
s a
squ
are.
See
stu
den
ts’w
ork
.
6MG
2.3
Answers (Lesson 10-6)
Chapter 10 A16 Glencoe California Mathematics, Grade 6
An
swer
s
Cla
ssif
y ea
ch q
uad
rila
tera
l u
sin
g th
e n
ame
that
bes
t d
escr
ibes
it.
1.2.
3.
rect
ang
lep
aral
lelo
gra
mq
uad
rila
tera
l
4.5.
6.
trap
ezo
id
rho
mbu
sp
aral
lelo
gra
m
ALG
EBR
AF
ind
th
e m
issi
ng
angl
e m
easu
re i
n e
ach
qu
adri
late
ral.
7.77
°8.
102°
9.13
0°
10.
55°
11.
70°
12.
28°
Fin
d t
he
mis
sin
g m
easu
re i
n e
ach
qu
adri
late
ral
wit
h t
he
give
n a
ngl
em
easu
res.
13.
63.2
°,56
°,11
1.7°
,x°
129.
1°14
.31
.7°,
x°,1
61.3
°,51
.4°
115.
6°
15.
x°,1
22.4
°,53
.7°,
90°
93.9
°16
.83
.7°,
137.
2°,x
°,28
.5°
110.
6°
17.
ALG
EBR
AF
ind
m�
Cin
qu
adri
late
ral
AB
CD
if m
�A
�11
0°,m
�B
�88
°,an
d m
�D
�55
°.10
7°18
.A
LGEB
RA
Wh
at i
s m
�Z
in q
uad
rila
tera
l W
XY
Zif
m�
W�
86°,
m�
X�
88°,
and
m�
Y�
92°?
94°
ALG
EBR
AF
ind
th
e va
lue
of x
in e
ach
qu
adri
late
ral.
19.
113.
520
.12
021
.30
3x˚
3x˚
3x˚
3x˚
60˚
60˚
x˚
x˚68
˚65
˚
x˚x˚
152˚ x˚
120˚11
0˚60
˚
x˚
125˚
x˚
130˚
50˚̊
50˚̊
x˚12
6˚78
˚̊54
˚̊
x˚
107˚
96˚̊
80˚̊
x˚
NA
ME
____
____
____
____
____
____
____
____
____
____
DA
TE
___
____
____
___
PE
RIO
D
____
_
Prac
tice
Qu
adri
late
rals
Cha
pter
10
41G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–6
pygp
10-6
6MG
2.3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Skill
s Pr
actic
eQ
uad
rila
tera
ls
Cha
pter
10
40G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-6
Cla
ssif
y th
e q
uad
rila
tera
l u
sin
g th
e n
ame
that
bes
td
escr
ibes
it.
1.2.
3.
par
alle
log
ram
rect
ang
lesq
uar
e
4.5.
6.
trap
ezo
idq
uad
rila
tera
lrh
om
bus
7.8.
9.
par
alle
log
ram
rho
mbu
str
apez
oid
Fin
d t
he
mis
sin
g an
gle
mea
sure
of
each
qu
adri
late
ral.
10.
11.
12.
128�
40�
115�
13.
14.
15.
77�
75�
116�
64˚
x˚
77˚99
˚10
9˚
x˚
72˚12
1˚
x˚
89˚ 92˚
64˚
x˚13
5˚11
0˚ 75˚
x˚
52˚
x˚
6MG
2.3
Answers (Lesson 10-6)
Chapter 10 A17 Glencoe California Mathematics, Grade 6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
10
43G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–6
pygp
10-6
The
Co
lorm
atch
Sq
uar
eT
o w
ork
this
pu
zzle
,cu
t ou
t th
e 16
til
es a
t th
e bo
ttom
of
this
pag
e.T
he
goal
of
the
puzz
le i
s to
cre
ate
a sq
uar
e so
th
at t
he
side
s of
an
y pa
ir o
f ad
jace
nt
tile
sm
atch
.You
are
not
all
owed
to
rota
te a
ny
of t
he
tile
s.
1.C
ompl
ete
the
solu
tion
to
the
colo
rmat
ch s
quar
e pu
zzle
bel
ow.
2.F
ind
at l
east
on
e ot
her
sol
uti
on i
n w
hic
h t
he
A t
ile
is i
n t
he
upp
er l
eft
corn
er.
Th
ere
are
10 o
ther
so
luti
on
s w
ith
A in
th
e u
pp
er le
ft c
orn
er a
nd
50
un
iqu
e so
luti
on
s in
all.
AD
PN
BG
LO
H
M
C
IK
J
FE
A D
Whi
tesq
uare
sm
atch
.
P N
B G L O
H M C I
K J F E
6MG
2.3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Wor
d Pr
oble
m P
ract
ice
Qu
adri
late
rals
Cha
pter
10
42G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-6
1.K
ITES
A k
ite
is s
how
n b
elow
.Wh
at i
sth
e be
st n
ame
to c
lass
ify
the
shap
e of
the
kite
? E
xpla
in.
qu
adri
late
ral;
Sam
ple
an
swer
:T
he
kite
is a
fo
ur-
sid
ed f
igu
re.I
td
oes
no
t fi
t th
e d
escr
ipti
on
of
any
oth
er q
uad
rila
tera
l in
th
ele
sso
n.
2.M
APS
A m
ap s
how
ing
the
road
con
nec
tin
g th
e to
wn
s of
Pik
e,H
uds
on,
Pla
cid,
and
Alt
on i
s sh
own
.Th
e ro
adco
nn
ecti
ng
Pik
e an
d H
uds
on i
s pa
rall
elto
th
e ro
ad c
onn
ecti
ng
Alt
on a
nd
Pla
cid.
Wh
at i
s th
e be
st n
ame
tocl
assi
fy t
he
shap
e of
th
e ro
ads
con
nec
tin
g th
e fo
ur
tow
ns?
Exp
lain
.
trap
ezo
id;
Sam
ple
an
swer
:Tw
oo
f th
e ro
ads
are
go
ing
Eas
t to
Wes
t,so
th
ey a
re p
aral
lel.
So
,th
e q
uad
rila
tera
l is
a tr
apez
oid
.
Huds
onPi
ke
Plac
idAl
tonN
3.A
RT
A p
ictu
re f
ram
e is
sh
own
bel
ow.
Wh
at i
s th
e be
stn
ame
to c
lass
ify
the
shap
e of
th
e fr
ame?
squ
are
1 ft
1 ft
4.SC
HO
OL
SUPP
LIES
Th
e si
de v
iew
of
aner
aser
is
show
n b
elow
.Wh
at i
s th
e be
stn
ame
to c
lass
ify
the
shap
e of
th
eer
aser
?
par
alle
log
ram
5.PA
RTY
Th
e fr
ont
of a
bir
thda
y pa
rty
invi
tati
on i
s sh
own
bel
ow.F
ind
the
mea
sure
of
the
mis
sin
g an
gle.
60�
60˚
120˚
120˚
x˚PA
RTY!
6.TA
BLE
Th
e to
p of
Mr.
Bau
tist
a’s
new
coff
ee t
able
is
show
n b
elow
.Fin
d th
em
easu
re o
f th
e m
issi
ng
angl
e.
80�
60˚
120˚
100˚x˚
6MG
2.3
Answers (Lesson 10-6)
Chapter 10 A18 Glencoe California Mathematics, Grade 6
An
swer
s
Exer
cise
s
Exam
ple
1
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Sim
ilar
Fig
ure
s
Cha
pter
10
45G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–7
pygp
10-7
If M
NO
P�
RS
TU
,fin
d t
he
len
gth
of
S�T�
.
Sin
ce t
he
two
figu
res
are
sim
ilar
,th
e ra
tios
of
thei
r co
rres
pon
din
gsi
des
are
equ
al.Y
ou c
an w
rite
an
d so
lve
a pr
opor
tion
to
fin
d S�
T�.
� UPO T�
��N S
TO �W
rite
a pr
opor
tion.
� 27 8��
� n5 �Le
t n
repr
esen
t th
e le
ngth
of
ST
.T
hen
subs
titut
e.
7n�
28(5
)F
ind
the
cros
s pr
oduc
ts.
7n�
140
Sim
plify
.
n�
20D
ivid
e ea
ch s
ide
by 7
.
Th
e le
ngt
h o
f S�
T�is
20
feet
.
Fin
d t
he
valu
e of
xin
eac
h p
air
of s
imil
ar f
igu
res.
1.2.
15 m
6 ft
3.4.
18 y
d15
in.
6 in
.
5 in
.
18 in
.
BC D
A
FG H
E
x
9 yd
5 yd
10 y
dM
N OP
RS T
U
x
2 ft
4 ft
I
G
K
H
L
J
x
12 ft
3 m
5 m
A
B
F
C
D
Ex
9 m
Fig
ures
tha
t ha
ve t
he s
ame
shap
e bu
t no
t ne
cess
arily
the
sa
me
size
are
sim
ilar
figur
es.T
he s
ymbo
l �m
eans
is
sim
ilar
to.Y
ou c
an u
se p
ropo
rtio
ns t
o fin
d th
e m
issi
ng
leng
th o
f a
side
in a
pai
r of
sim
ilar
figur
es.
For
exa
mpl
e �
AB
C�
�D
EF.
Cor
resp
ondi
ng a
ngle
sC
orre
spon
ding
sid
es
� A
��
D� 15 0�
��4 8�
��3 6�
�B
��
E
�C
��
F
7 ft
5 ft
28 ft
MN O
P
RS T
U
4
3A
B
FC
D
E
810
6
5
6NS
1.3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Less
on R
eadi
ng G
uide
S
imila
r F
igu
res
Cha
pter
10
44G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-7
Get
Rea
dy
for
the
Less
on
Com
ple
te t
he
Min
i L
ab i
n y
our
text
boo
k.W
rite
you
r an
swer
s b
elow
.
1.A�
B�on
th
e sm
alle
r re
ctan
gle
mat
ches
E�F�
on t
he
larg
er r
ecta
ngl
e.N
ame
all
pair
s of
mat
chin
g si
des
in e
ach
pai
r of
fig
ure
s.A�
B�an
d E�
F�,B�
C�an
d F�
G�,
C�D�
and
G�H�
,D�A�
and
H�E�
,R�T�
and
X�Z�,
S�T�
and
Y�Z�
,R�S�
and
X�Y�
2.W
rite
eac
h r
atio
in
sim
ples
t fo
rm.
a.�A E
B F�;�
FBGC �
;�HD
GC �;�
EAHD �
�1 3� ;�1 3� ;
�1 3� ;�1 3�
b.
�R XYS �
;�S Y
T Z�;�
R XZT �
2;2;
2
3.W
hat
do
you
not
ice
abou
t th
e ra
tios
of
mat
chin
g si
des.
Th
ey a
re e
qu
al.
4.N
ame
all
pair
s of
mat
chin
g an
gles
in
th
e fi
gure
s ab
ove.
Wh
at d
o yo
un
otic
e ab
out
the
mea
sure
of
thes
e an
gles
?�
A a
nd
�E
,�B
,an
d �
F,�
C a
nd
�G
,�D
an
d �
H;
�R
an
d �
X,�
T,an
d �
Z,�
S,a
nd
�Y
;Th
ey a
re e
qu
al.
5.M
AK
E A
CO
NJE
CTU
RE
abou
t fi
gure
s th
at h
ave
the
sam
e sh
ape
but
not
n
eces
sari
ly t
he
sam
e si
ze.
Sam
ple
an
swer
:S
imila
r fi
gu
res
hav
eco
rres
po
nd
ing
sid
es t
hat
fo
rm e
qu
al r
atio
s an
d t
hei
r co
rres
po
nd
ing
ang
les
are
con
gru
ent.
Rea
d t
he
Less
on
6.W
rite
th
e st
atem
ent
�A
BC
��
DE
Fin
wor
ds.
Tria
ng
le A
BC
is s
imila
r to
tria
ng
le D
EF
.
7.W
rite
th
e st
atem
ent
�A
��
Din
wor
ds.
An
gle
Ais
co
ng
ruen
t to
an
gle
D.
8.S
upp
ose
you
kn
ow t
hat
tw
o fi
gure
s ar
e si
mil
ar,a
nd
that
th
e fo
llow
ing
corr
espo
ndi
ng
side
s ar
e pr
opor
tion
al:s
ide
JK
corr
espo
nds
to
side
DE
,an
dsi
de K
Lco
rres
pon
ds t
o si
de E
F.H
ow w
ould
you
wri
te a
pro
port
ion
to
fin
dth
e le
ngt
h o
f si
de K
Lif
th
e le
ngt
hs
of a
ll o
ther
sid
es a
re k
now
n?
Sam
ple
an
swer
:� DJK
E��
�K EFL �
Rem
emb
er W
hat
Yo
u L
earn
ed9.
Th
ink
of a
rea
l-li
fe e
xam
ple
that
you
cou
ld m
easu
re u
sin
g in
dire
ct
mea
sure
men
t if
you
wer
e gi
ven
a m
inia
ture
rep
lica
of
you
r ex
ampl
e.E
xpla
in h
ow y
ou c
ould
fin
d an
un
know
n m
easu
rem
ent
usi
ng
know
n
mea
sure
men
ts o
f yo
ur
exam
ple
and
the
mea
sure
men
ts o
f th
e re
plic
a.S
ee s
tud
ents
’w
ork
.Fo
r ex
amp
le,t
he
bas
e o
f th
e E
mp
ire
Sta
te B
uild
ing
is 7
,240
met
ers
by 1
29 m
eter
s,an
d t
he
build
ing
is 4
43.2
met
ers
to t
he
top
of
the
ligh
tnin
g r
od
.Yo
u c
ou
ld u
se a
rep
lica
of
the
Em
pir
e S
tate
Bu
ildin
g,
mea
sure
th
e b
ase
of
the
mo
del
an
d s
et u
p a
pro
po
rtio
n u
sin
g t
he
hei
gh
to
f th
e m
od
el t
o f
ind
th
e h
eig
ht
of
the
Em
pir
e S
tate
Bu
ildin
g.
6NS
1.3
Answers (Lesson 10-7)
Chapter 10 A19 Glencoe California Mathematics, Grade 6
1.W
hic
h r
ecta
ngl
e is
sim
ilar
to
rect
angl
e R
ST
U?
rect
ang
le E
FG
H
2.W
hic
h t
rian
gle
is s
imil
ar t
o tr
ian
gle
XY
Z?
tria
ng
le F
GH
Fin
d t
he
valu
e of
xin
eac
h p
air
of s
imil
ar f
igu
res.
3.4.
24
2.8
5.6.
54.
5
7.FL
AG
POLE
ST
ash
a w
ants
to
fin
d th
e h
eigh
t of
the
flag
pole
at
sch
ool.
On
e m
orn
ing,
she
dete
rmin
es t
he
flag
pole
cas
ts a
sh
adow
of
12 f
eet.
If T
ash
a is
5 f
eet
tall
an
d ca
sts
a sh
adow
of
3 fe
et,w
hat
is
the
hei
ght
of t
he
flag
pole
?20
ft
12 ft
x ft
3 ft
5 ft
4.2
mm
1.5
mm
12.6
mm
x m
m15
in.
8 in
.24
in.
x in
.
2 ft
5 ft
7 ft
x ft
6 cm
12 c
m12
cm
x cm
X
YZ
3024
PR
T10
14
C
F
HG
B
A32
3526
28
RS T
U3
5
AB C
D5
5
EF
MN
QP
GH6
8
102
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice
Sim
ilar
Fig
ure
s
Cha
pter
10
47G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–7
pygp
10-7
6NS
1.3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Skill
s Pr
actic
eS
imila
r F
igu
res
Cha
pter
10
46G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-7
Fin
d t
he
valu
e of
xin
eac
h p
air
of s
imil
ar f
igu
res.
1.2.
8 ft
21 m
3.4.
21 f
t30
cm
5.6.
6 m
m16
in.
Det
erm
ine
wh
eth
er e
ach
pai
r of
fig
ure
s is
sim
ilar
.Ju
stif
y yo
ur
answ
er.
7.8.
yes;
Sam
ple
an
swer
:n
o;
Sam
ple
an
swer
:� 28 4�
��1 45 0�
� 19 8��
� 17 4� ;
corr
esp
on
din
gan
gle
s ar
e co
ng
ruen
t.
24 m
40 m
15 m
8 m
D
F
EA
C
B
7 cm
9 cm
14 c
m
18 c
m
15 in
.
12 in
.
20 in
.
BC
DA
EF
GH
x
6 m
m
4 m
m
M
OQ
N
P
Rx
9 m
m
10 c
m
7 cm
21 c
m
BC
DA
FG
HE
x
12 ft
14 ft
A
B
E
CF
G
x
18 ft
H
D
7 m
3 mN
M
R
O
Q
P
x9
m4
ft
3 ftA
B
F
C
D
Ex
6 ft
6NS
1.3
Answers (Lesson 10-7)
Chapter 10 A20 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
10
49G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–7
pygp
10-7
Sim
ilar
Fig
ure
s an
d A
reas
Th
e ar
eas
of t
wo
sim
ilar
fig
ure
s ar
e re
late
d in
a
spec
ial
way
.Su
ppos
e th
at r
ecta
ngl
e A
is
2 u
nit
s by
3u
nit
s an
d re
ctan
gle
B i
s 4
un
its
by 6
un
its.
Th
e ar
ea o
f re
ctan
gle
A i
s 2
�3
�6
un
its2
.
Th
e ar
ea o
f re
ctan
gle
B i
s 4
�6
�24
un
its2
.
Th
e le
ngt
hs
of t
he
side
s of
rec
tan
gle
B a
re t
wic
e th
ose
of
rect
angl
e A
an
d th
e ar
ea o
f re
ctan
gle
B i
s fo
ur
tim
es t
hat
of
rect
angl
e A
.
Sk
etch
fig
ure
B s
imil
ar t
o fi
gure
A a
nd
sat
isfy
ing
the
give
n c
ond
itio
n.
1.R
ecta
ngl
e B
has
six
teen
tim
es t
he
area
of
rect
angl
e A
.
2.S
quar
e B
has
an
are
a th
at i
s 4
tim
es t
hat
of
squ
are
A.
3.C
ircl
e B
has
an
are
a fo
ur
tim
es t
hat
of
circ
le A
.
Circ
le B
Circ
le A
1.5
Squ
are
BS
quar
e A
2
2
Rec
tang
le B
Rec
tang
le A
31
Rec
tang
le B
Rec
tang
le A
36
42
6NS
1.3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Wor
d Pr
oble
m P
ract
ice
Sim
ilar
Fig
ure
s
Cha
pter
10
48G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-7
MO
DEL
CA
RS
For
Exe
rcis
es 1
an
d 2
,use
th
e fo
llow
ing
info
rmat
ion
.A s
cale
mod
el r
acin
g ca
r is
11
inch
es l
ong,
3 in
ches
wid
e,an
d 2
in
ches
tal
l.T
he
actu
al r
acin
g ca
r is
sh
own
at
the
righ
t.
PHO
TOG
RA
PHY
For
Exe
rcis
es 3
–4,u
se t
he
give
n
info
rmat
ion
.Jam
es w
ants
to
enla
rge
a p
hot
ogra
ph
th
at
is 6
in
ches
wid
e an
d 4
in
ches
tal
l so
th
at i
t fi
ts i
nto
th
e fr
ame
show
n.
30 in
.
22 ft
1.H
ow w
ide
is t
he
actu
al r
acin
g ca
r?
6 ft
2.H
ow t
all
is t
he
actu
al r
acin
g ca
r?4
ft
3.H
ow t
all
mu
st t
he
fram
e be
for
th
epi
ctu
re t
o fi
t?20
in.
4.S
upp
ose
Jam
es c
uts
1 i
nch
fro
m
the
wid
th o
f th
e ph
oto,
so t
hat
it
is 5
in
ches
wid
e,be
fore
he
mak
es t
he
enla
rgem
ent.
How
tal
l w
ill
the
fram
eh
ave
to b
e fo
r th
e pi
ctu
re t
o fi
t?24
in.
5.M
APS
A m
ap b
elow
sh
ows
the
tow
ns
ofD
over
,Bu
tler
,an
d L
odi.
If t
he
actu
aldi
stan
ce b
etw
een
Dov
er a
nd
Bu
tler
is
24 m
iles
,how
far
is
it f
rom
Dov
er t
oL
odi?
32 m
iLo
di
Butle
rDo
ver
4 in
. 3 in
.
6.B
LUEP
RIN
TSA
blu
epri
nt
for
a h
ouse
is
show
n b
elow
.If
the
fron
t of
th
e h
ouse
is a
ctu
ally
30
feet
wid
e,h
ow t
all
is t
he
hou
se?
35 f
t12
in.
14 in
.
6NS
1.3
Answers (Lesson 10-7)
Chapter 10 A21 Glencoe California Mathematics, Grade 6
Exam
ple
s
Exer
cise
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Po
lyg
on
s an
d T
esse
llati
on
s
Cha
pter
10
51G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–8
pygp
10-8
Det
erm
ine
wh
eth
er e
ach
fig
ure
is
a p
olyg
on.I
f it
is,
clas
sify
th
ep
olyg
on a
nd
sta
te w
het
her
it
is r
egu
lar.
If i
t is
not
a p
olyg
on,
exp
lain
wh
y.
Th
e fi
gure
has
5 c
ongr
uen
t si
des
Th
e fi
gure
is
not
a p
olyg
onan
d 5
con
gru
ent
angl
es.I
t is
a
beca
use
it
has
sid
es t
hat
ove
rlap
.re
gula
r pe
nta
gon
.
Det
erm
ine
wh
eth
er e
ach
fig
ure
is
a p
olyg
on.I
f it
is,
clas
sify
th
ep
olyg
on a
nd
sta
te w
het
her
it
is r
egu
lar.
If i
t is
not
a p
olyg
on,e
xpla
inw
hy.
1.2.
3.
tria
ng
leN
ot
a p
oly
go
n;
it
has
a c
urv
ed s
ide.
reg
ula
r p
enta
go
n
4.5.
6.
No
t a
po
lyg
on
;it
isre
gu
lar
qu
adri
late
ral
hex
ago
nn
ot
clo
sed
.(s
qu
are)
120˚
A p
oly
go
nis
a s
impl
e, c
lose
d fig
ure
form
ed b
y th
ree
or m
ore
stra
ight
line
s.A
sim
ple
figur
e do
es n
otha
ve li
nes
that
cro
ss e
ach
othe
r.Yo
u ha
ve d
raw
n a
clos
ed f
igur
e w
hen
your
pen
cil e
nds
up w
here
itst
arte
d.P
olyg
ons
can
be c
lass
ified
by
the
num
ber
of s
ides
the
y ha
ve.
A p
olyg
on t
hat
has
all s
ides
con
grue
nt a
nd a
ll an
gles
con
grue
nt is
cal
led
a re
gu
lar
po
lyg
on
.
deca
gon
10 s
ides
nona
gon
9 si
des
octa
gon
8 si
des
hept
agon
7 si
des
hexa
gon
6 si
des
pent
agon
5 si
des
6MR
2.2
, 6A
F3.
2
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Less
on R
eadi
ng G
uide
Po
lyg
on
s an
d T
esse
llati
on
s
Cha
pter
10
50G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-8
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n a
t th
e to
p o
f p
age
546
in y
our
text
boo
k.W
rite
you
r an
swer
s b
elow
.
1.F
ind
the
diff
eren
ce b
etw
een
th
e sh
apes
of
the
stat
es i
n G
rou
p 1
and
the
shap
es o
f th
e st
ates
in
Gro
up
2.S
amp
le a
nsw
er:T
he
bo
rder
s o
f st
ates
in G
rou
p 1
are
str
aig
ht.
Th
e b
ord
ers
of
stat
es in
Gro
up
2 a
re n
ot
stra
igh
t.
2.W
hy
do m
ost
stat
es h
ave
bou
nda
ries
th
at a
re n
ot s
trai
ght
lin
e se
gmen
ts?
Sam
ple
an
swer
:Th
ey u
se n
atu
ral b
ou
nd
arie
s lik
e ri
vers
an
dla
kes.
Rea
d t
he
Less
on
3.H
ow m
any
stra
igh
t li
nes
can
a p
olyg
on h
ave?
thre
e o
r m
ore
4.W
hat
is
a si
mpl
e fi
gure
?S
amp
le a
nsw
er:
a fi
gu
re t
hat
do
es n
ot
hav
e lin
es t
hat
cro
ss e
ach
oth
er
5.W
hen
you
dra
w a
fig
ure
,how
can
you
tel
l w
het
her
or
not
it
is c
lose
d?S
amp
le a
nsw
er:T
he
fig
ure
is c
lose
d if
,wh
en y
ou
dra
w it
,th
ep
enci
l en
ds
up
wh
ere
it s
tart
ed.
6.H
ow d
o yo
u f
ind
the
sum
of
the
angl
e m
easu
res
in a
reg
ula
r po
lygo
n?
Sam
ple
an
swer
:D
raw
all
of
the
dia
go
nal
s fr
om
on
e ve
rtex
,co
un
t th
e n
um
ber
of
tria
ng
les
form
ed,a
nd
mu
ltip
ly b
y 18
0�.
7.In
th
is l
esso
n,t
he
term
s ve
rtex
and
vert
ices
are
use
d.H
ow a
re t
he
term
sre
late
d?S
amp
le a
nsw
er:
Ver
tice
sis
th
e p
lura
l of
vert
ex.
Rem
emb
er W
hat
Yo
u L
earn
ed8.
Usi
ng
dot
pape
r,dr
aw a
tes
sell
atio
n d
iffe
ren
t fr
om t
he
ones
sh
own
in
th
isle
sson
.You
can
use
all
th
e sa
me
shap
e or
you
can
use
com
bin
atio
ns
ofsh
apes
th
at f
orm
pat
tern
s.S
har
e yo
ur
wor
k w
ith
you
r cl
ass.
See
stu
den
ts’w
ork
.
6MR
2.2
, 6A
F3.
2
Answers (Lesson 10-8)
Chapter 10 A22 Glencoe California Mathematics, Grade 6
An
swer
s
Det
erm
ine
wh
eth
er e
ach
fig
ure
is
a p
olyg
on.I
f it
is,
clas
sify
th
e p
olyg
onan
d s
tate
wh
eth
er i
t is
reg
ula
r.If
it
is n
ot a
pol
ygon
,exp
lain
wh
y.
1.2.
3.
4.5.
6.
Fin
d t
he
mea
sure
of
an a
ngl
e in
eac
h p
olyg
on i
f th
e p
olyg
on i
s re
gula
r.R
oun
d t
oth
e n
eare
st t
enth
of
a d
egre
e if
nec
essa
ry.
7.do
deca
gon
8.
14-g
on9.
18-g
on10
.36
-gon
(12-
side
d)15
0°15
4.3°
160°
170°
Cla
ssif
y th
e p
olyg
ons
that
are
use
d t
o cr
eate
eac
h t
esse
llat
ion
.
11.
12.
13.
Wh
at i
s th
e pe
rim
eter
of
a re
gula
r de
cago
n w
ith
sid
es 6
.2 m
eter
s lo
ng?
62 m
14.
Fin
d th
e pe
rim
eter
of
a re
gula
r h
exag
on h
avin
g si
des
5�2 3�
inch
es l
ong.
34 in
.
KIT
ESF
or E
xerc
ises
15–
17,u
se t
he
foll
owin
g in
form
atio
n.A
kit
e m
anu
fact
ure
r m
akes
k
ites
in
th
e sh
ape
of t
he
figu
re s
how
n.
15.
Cla
ssif
y th
e sh
ape
of t
he
kite
.q
uad
rila
tera
l
16.
If �
K�
�T
and
�E
�30
°,fi
nd
m�
Kan
d m
�T
.m
�K
�m
�T
�12
0°
17.
Can
a t
esse
llat
ion
be
mad
e by
usi
ng
the
shap
e of
th
e ki
te?
Just
ify
you
r an
swer
.ye
s;36
0°is
div
isib
le b
y th
e m
easu
re o
f ea
ch a
ng
le in
th
e fi
gu
re.
KT
I E
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice
Po
lyg
on
s an
d T
esse
llati
on
s
Cha
pter
10
53G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–8
pygp
10-8
qu
adri
late
ral;
no
t re
gu
lar
pen
tag
on
;n
ot
reg
ula
req
uila
tera
ltr
ian
gle
;re
gu
lar
No
t a
po
lyg
on
;th
e fi
gu
re is
no
t si
mp
le.
reg
ula
r h
exag
on
No
t a
po
lyg
on
;th
e fi
gu
re
has
cu
rved
sid
es.
squ
ares
an
d
equ
ilate
ral
tria
ng
les
reg
ula
rh
exag
on
s an
deq
uila
tera
ltr
ian
gle
s
6MR
2.2
, 6A
F3.
2
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Skill
s Pr
actic
eP
oly
go
ns
and
Tes
sella
tio
ns
Cha
pter
10
52G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-8
Det
erm
ine
wh
eth
er e
ach
fig
ure
is
a p
olyg
on.I
f it
is,
clas
sify
th
e p
olyg
onan
d s
tate
wh
eth
er i
t is
reg
ula
r.If
it
is n
ota
pol
ygon
,exp
lain
wh
y.
1.2.
3.
qu
adri
late
ral
No
t a
po
lyg
on
;th
ere
gu
lar
hex
ago
nfi
gu
re is
cir
cula
r.
4.5.
6.
No
t a
po
lyg
on
;th
eeq
uila
tera
l (re
gu
lar)
pen
tag
on
fig
ure
is n
ot
clo
sed
.tr
ian
gle
7.8.
9.
reg
ula
r h
epta
go
no
ctag
on
No
t a
po
lyg
on
;th
efi
gu
re is
no
t cl
ose
d.
Fin
d t
he
mea
sure
of
an a
ngl
e in
eac
h p
olyg
on.
10.
regu
lar
15-g
on15
6�11
.re
gula
r 18
-gon
160�
12.
regu
lar
24-g
on16
5�
Cla
ssif
y th
e p
olyg
ons
that
are
use
d t
o cr
eate
eac
h t
esse
llat
ion
.
13.
14.
squ
are
and
tri
ang
leh
exag
on
an
d t
rian
gle
15.
Wh
at i
s th
e pe
rim
eter
of
a re
gula
r pe
nta
gon
wit
h s
ides
8.4
in
ches
lon
g?42
in.
6MR
2.2
, 6A
F3.
2
Answers (Lesson 10-8)
Chapter 10 A23 Glencoe California Mathematics, Grade 6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
10
55G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–8
pygp
10-8
Tess
ella
ted
Pat
tern
s fo
r So
lid S
hap
esT
esse
llat
ion
s m
ade
from
equ
ilat
eral
tri
angl
es c
an b
e u
sed
to b
uil
dth
ree-
dim
ensi
onal
sh
apes
.In
Exe
rcis
e 1,
you
sh
ould
get
a s
hap
e li
keth
e on
e sh
own
at
the
righ
t.It
is
call
ed a
pyr
amid
.
Cop
y ea
ch p
atte
rn.C
reas
e th
e p
atte
rn a
lon
g th
e li
nes
.T
hen
fol
low
dir
ecti
ons
for
fold
ing
the
pat
tern
.Use
tap
e to
se
cure
th
e fo
lded
par
ts.W
hen
you
hav
e fi
nis
hed
eac
h m
odel
,d
escr
ibe
it i
n w
ord
s.
1.F
old
5 ov
er 1
.R
epea
t,in
th
is o
rder
:fo
ld 6
ove
r 7,
fold
2 o
ver
6.p
yram
id w
ith
fo
ur
tria
ng
ula
r fa
ces
2.C
ut
betw
een
4 a
nd
5.T
hen
fol
d 5
over
3.
Rep
eat
in t
his
ord
er:
fold
6 o
ver
5,fo
ld 7
ove
r 12
,an
dfo
ld 2
ove
r 9.
do
ub
le p
yram
id w
ith
six
tr
ian
gu
lar
face
s
3.C
ut
betw
een
1 a
nd
2 an
d be
twee
n
14 a
nd
15.T
hen
fol
d 15
ove
r 14
.R
epea
t,in
th
is o
rder
:fo
ld 1
ove
r 2,
fold
4 o
ver
3,fo
ld 1
1 ov
er 1
,fo
ld 1
6 ov
er 5
,an
dfo
ld 1
2 ov
er 1
3.p
enta
go
nal
sh
ape
wit
h
ten
tri
ang
ula
r fa
ces
1 57
10
14
69
11
1213
15
16
2
8
34
3 810
79
12
2
4
11
56
1
1 35
24 7
6
6MR
2.2
, 6A
F3.
2
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Wor
d Pr
oble
m P
ract
ice
Po
lyg
on
s an
d T
esse
llati
on
s
Cha
pter
10
54G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-8
1.R
OYA
LTY
Th
e ou
tlin
e of
a c
row
n w
orn
by a
kin
g is
sh
own
bel
ow.I
s th
e fi
gure
a po
lygo
n?
If i
t is
,cla
ssif
y th
e po
lygo
nan
d st
ate
wh
eth
er i
t is
reg
ula
r.If
it
isn
ota
poly
gon
,exp
lain
wh
y.
yes;
no
nag
on
;n
ot
reg
ula
r
2.A
LCH
EMY
Th
e sy
mbo
l sh
own
is
one
of t
he
sign
s fo
r sa
lt a
lkal
iu
sed
in
17th
-cen
tury
ch
emis
try.
Is t
he
sym
bol
a po
lygo
n?
If i
t is
,cla
ssif
y th
e po
lygo
nan
d st
ate
wh
eth
er i
t is
reg
ula
r.If
it
isn
ota
poly
gon
,exp
lain
wh
y.
yes;
oct
ago
n;
no
t re
gu
lar
3.JE
WEL
RYT
he
sym
bol
show
n i
s of
ten
use
d to
rep
rese
nt
gem
s.Is
th
e sy
mbo
l a
poly
gon
? If
it
is,c
lass
ify
the
poly
gon
and
stat
e w
het
her
it
is r
egu
lar.
If i
t is
not
a po
lygo
n,e
xpla
in w
hy.
No
;th
e fi
gu
re h
as o
verl
app
ing
sid
es.
4.SY
MB
OLS
Th
e 5-
poin
ted
star
sh
own
has
side
s of
equ
al l
engt
h.I
s th
e sy
mbo
l a
poly
gon
? If
it
is,c
lass
ify
the
poly
gon
and
stat
e w
het
her
it
is r
egu
lar.
If i
t is
not
a po
lygo
n,e
xpla
in w
hy.
yes;
dec
ago
n;
no
t re
gu
lar
5.ST
AIR
ST
he
figu
re s
how
s a
side
vie
w o
fa
set
of s
tair
s.Is
th
e fi
gure
a p
olyg
on?
If i
t is
,cla
ssif
y th
e po
lygo
n a
nd
stat
ew
het
her
it
is r
egu
lar.
If i
t is
not
apo
lygo
n,e
xpla
in w
hy.
yes;
14-g
on
;n
ot
reg
ula
r
6.TE
SSEL
LATI
ON
SId
enti
fy t
he
poly
gon
sth
at a
re u
sed
to c
reat
e th
e te
ssel
lati
onsh
own
in
th
e fi
gure
.
tria
ng
le a
nd
hex
ago
n
6MR
2.2
, 6A
F3.
2
Answers (Lesson 10-8)
Chapter 10 A24 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DA
TE
___
____
____
___
PE
RIO
D
____
_
Less
on R
eadi
ng G
uide
Tran
slat
ion
s
Cha
pter
10
57G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–9
pygp
10-9
Get
Rea
dy
for
the
Less
on
Com
ple
te t
he
Min
i L
ab a
t th
e to
p o
f p
age
553
in y
our
text
boo
k.W
rite
you
r an
swer
s b
elow
.
1.T
race
th
e h
oriz
onta
l an
d ve
rtic
al p
ath
bet
wee
n c
orre
spon
din
g ve
rtic
es.
Wh
at d
o yo
u n
otic
e?T
hey
hav
e th
e sa
me
pat
h,5
un
its
to t
he
rig
ht
and
2 u
nit
s d
ow
n.
2.A
dd 5
to
each
x-c
oord
inat
e of
th
e ve
rtic
es o
f th
e or
igin
al f
igu
re.T
hen
subt
ract
2 f
rom
eac
h y
-coo
rdin
ate
of t
he
vert
ices
of
the
orig
inal
fig
ure
.W
hat
do
you
not
ice?
T
he
resu
lt is
th
e co
ord
inat
es o
f th
eve
rtic
es o
f th
e fi
gu
re in
its
new
po
siti
on
.
Rea
d t
he
Less
on
3.W
hen
tra
nsl
atin
g a
figu
re,w
hat
do
you
kn
ow a
bou
t ev
ery
poin
t of
th
eor
igin
al f
igu
re?
Sam
ple
an
swer
:It
mov
es t
he
sam
e d
ista
nce
and
in t
he
sam
e d
irec
tio
n.
4.C
an a
fig
ure
be
turn
ed i
n a
tra
nsl
atio
n?
Exp
lain
.n
o;
Sam
ple
an
swer
:Wh
en a
fig
ure
is t
urn
ed,e
very
po
int
do
es n
ot
mov
e in
th
e sa
me
dir
ecti
on
.
5.W
hat
not
atio
n i
s u
sed
to i
ndi
cate
th
e ve
rtic
es o
f a
tran
slat
ed f
igu
re?
Sam
ple
an
swer
:P
rim
e sy
mb
ols
are
use
d w
ith
th
e ve
rtic
es o
fth
e tr
ansl
ated
imag
e.6.
Wh
ich
fig
ure
is
a tr
ansl
atio
n o
f F
igu
re 1
—F
igu
re 2
or
Fig
ure
3?
Exp
lain
wh
y on
e fi
gure
is
a tr
ansl
atio
n a
nd
wh
y th
e ot
her
fig
ure
is
not
a t
ran
slat
ion
.F
igu
re 3
is a
tra
nsl
atio
n o
f F
igu
re 1
;S
amp
le a
nsw
er:
Eac
h p
oin
t in
Fig
ure
1 m
oves
4 u
nit
sd
ow
n a
nd
4 u
nit
s to
th
e le
ft (
�4,
�4)
.Fig
ure
2 is
no
t a
tran
slat
ion
of
Fig
ure
1.E
ach
po
int
in F
igu
re 1
do
es n
ot
mov
e th
e sa
me
dis
tan
ce a
nd
in t
he
sam
e d
irec
tio
n t
ocr
eate
Fig
ure
2.
Rem
emb
er W
hat
Yo
u L
earn
ed7.
Des
crib
e th
e tr
ansl
atio
n g
iven
by
the
orde
red
pair
(�
7,3)
.Th
ink
of a
way
to r
emem
ber
wh
ich
dir
ecti
on t
o tr
ansl
ate
wh
en t
he
x-co
ordi
nat
e of
th
eor
dere
d pa
ir d
escr
ibin
g th
e tr
ansl
atio
n i
s n
egat
ive.
Tran
slat
e 7
un
its
left
an
d 3
un
its
up
.See
stu
den
ts’w
ork
.
1 2
3
7MG
3.2
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
TI-7
3 A
ctiv
ityIn
teri
or
An
gle
s
Cha
pter
10
56G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-8
Use
you
r ca
lcul
ator
to
expl
ore
inte
rior
ang
les
of p
olyg
ons.
The
sum
of
the
mea
sure
s of
the
inte
rior
ang
les
of a
pol
ygon
wit
h n
side
s is
:Su
m �
(n�
2) �
180°
.
If th
e po
lygo
n is
reg
ular
, the
n th
e m
easu
re o
f ea
ch in
teri
or is
this
Sum
div
ided
by
n, o
r �S
u nm �.
Use
an
d th
ese
form
ulas
to c
ompl
ete
the
tabl
e be
low
.
Step
1C
lear
all
list
s.[M
EM]6
Step
2O
pen
the
Lis
t fea
ture
.
Step
3In
L1,
ent
er n
, the
num
ber
of s
ides
.
Pre
ss
afte
r ea
ch v
alue
.
Step
4In
L2,
ent
er th
e S
um o
f In
teri
or A
ngle
s fo
rmul
a.
Hig
hlig
ht L
2.
[TEX
T]"
Don
e [S
TAT]
1 2
180
[TEX
T]"
Don
e
Step
5H
ighl
ight
L3
and
ente
r th
e fo
rmul
a fo
r th
e m
easu
re o
f ea
ch a
ngle
.
[TEX
T]"
Don
e [S
TAT]
2[S
TAT]
1
[TEX
T]"
Don
e 1.
Che
ck th
at th
e an
gle
mea
sure
s fo
r th
e oc
tago
n ar
e co
rrec
t by
eval
uatin
g th
e ex
pres
sion
sw
hen
n�
8.D
o yo
ur c
alcu
latio
ns
mat
ch th
e lis
t val
ues?
Yes,
(8 �
2) �
180
�10
80,
�10880 �
�13
5.
2.D
escr
ibe
the
tren
ds y
ou
see
in th
e su
m a
nd th
e an
gle
mea
sure
col
umns
.
Sam
ple
an
swer
:Th
e su
m v
alu
es in
crea
se b
y 18
0 as
th
e n
um
ber
of
sid
esin
crea
ses
by 1
.T
he
ang
le m
easu
re a
lso
incr
ease
s bu
t it
is a
lway
s le
ss
than
180
.
EN
TE
RE
NT
ER
2nd
2nd
2nd
2nd
EN
TE
RE
NT
ER
2nd
)2n
d(
2nd
EN
TE
R
LIS
T
EN
TE
R2n
d
LIS
T Nam
e o
f P
oly
go
nE
ach
Ang
le(R
egul
ar P
oly
go
n)
3tr
iang
le18
0°60
°
4q
uad
rila
tera
l36
0°90
°
5p
enta
go
n54
0°10
8°
6h
exag
on
720°
120°
7h
epta
go
n90
0°�
128.
57°
8o
ctag
on
1,08
0°13
5°
9n
on
ago
n1,
260°
140°
10d
ecag
on
1,44
0°14
4°
No
. of
Sid
esS
um o
f In
teri
or
Ang
les
Answers (Lessons 10-8 and 10-9)
Chapter 10 A25 Glencoe California Mathematics, Grade 6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Skill
s Pr
actic
eTr
ansl
atio
ns
Cha
pter
10
59G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–9
pygp
10-9
1.T
ran
slat
e �
AB
C5
un
its
left
.2.
Tra
nsl
ate
rect
angl
e R
ST
U2
un
its
righ
tan
d 5
un
its
up.
3.T
ran
slat
e �
DE
F4
un
its
left
an
d 4.
Tra
nsl
ate
trap
ezoi
d L
MN
O5
un
its
righ
t4
un
its
dow
n.
and
3 u
nit
s do
wn
.
Tri
angl
e X
YZ
has
ver
tice
s X
(�4,
5),Y
(�1,
3),a
nd
Z(�
2,0)
.Fin
d t
he
vert
ices
of
XY
Z
afte
r ea
ch t
ran
slat
ion
.Th
en g
rap
h t
he
figu
re a
nd
its
tran
slat
ed i
mag
e.
5.5
un
its
dow
n6.
4 u
nit
s ri
ght,
3 u
nit
s do
wn
X(
�4,
0),
X(
0,2)
,Y
(�
1,�
2),
Y(
3,0)
,Z
(�
2,�
5)Z
(2,
�3)
Par
alle
logr
am R
ST
Uh
as v
erti
ces
R(�
1,�
3),S
(0,�
1),T
(4,�
1),a
nd
U(3
,�3)
.Fin
d t
he
vert
ices
of
RS
TU
af
ter
each
tra
nsl
atio
n.T
hen
grap
h t
he
figu
re a
nd
its
tra
nsl
ated
im
age.
7.3
un
its
left
,3 u
nit
s u
p8.
1 u
nit
rig
ht,
5 u
nit
s u
p
R(
�4,
0),
R(
0,2)
,S
(�
3,2)
,S
(1,
4),
T(
1,2)
,T
(5,
4),
U(
0,0)
U(
4,2)
y
xO
S'
R'
T'
U'
U
T
R
S
y
xO
S'
R'
T'
U'
U
T
R
S
y
xO
Y'
X'
X
Z'
Z
Y
y
xO Y'
X'
X
Z'
Z
Y
y
xOO
N
L
M
O'
N'
L'
M'
y
xO
D F
E
D'
F'
E'
y
xO
UT
RS
U'
T'
R'
S'
y
xO
B A
CB
'
A'
C'
7MG
3.2
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Tran
slat
ion
s
Cha
pter
10
58G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-9
Tri
angl
e A
BC
has
ver
tice
s A
(�4,
�2)
,B(�
2,0)
,an
d C
(�1,
�3)
.F
ind
th
e ve
rtic
es o
f tr
ian
gle
AB
C
afte
r a
tran
slat
ion
of
5 u
nit
sri
ght
and
2 u
nit
s u
p.
Add
5 t
o ea
ch x
-coo
rdin
ate.
Add
2 t
o ea
ch y
-coo
rdin
ate.
Th
e co
ordi
nat
es o
f th
e ve
rtic
es o
f �
AB
C
are
A(
1,0)
,B(
3,2)
,an
d C
(4,
�1)
.
1.T
ran
slat
e �
GH
I1
un
it l
eft
and
2.T
ran
slat
e re
ctan
gle
LM
NO
4 u
nit
s ri
ght
5 u
nit
s do
wn
.an
d 3
un
its
up.
Tri
angl
e R
ST
has
ver
tice
s R
(3,2
),S
(4,�
2),a
nd
T(1
,�1)
.Fin
d t
he
vert
ices
of
RS
T
afte
r ea
ch t
ran
slat
ion
.Th
en g
rap
h t
he
figu
re a
nd
its
tran
slat
ed i
mag
e.
3.5
un
its
left
,1 u
nit
up
4.3
un
its
left
,2 u
nit
s do
wn
R(
�2,
3),S
(�
1,�
1),T
(�
4,0)
R(
0,0)
,S(
1,�
4),T
(�
2,�
3)
y
xO
S'
T'
T
R'
R
S
y
xO
S'
T'
T
R'
R S
y
xO
M'
N'
L' O'
ON
LM
y
xO
G'
I'
H'H
IG
A t
ran
slat
ion
is t
he m
ovem
ent
of a
geo
met
ric f
igur
e in
som
e di
rect
ion
with
out
turn
ing
the
figur
e.W
hen
tran
slat
ing
a fig
ure,
eve
ry p
oint
of
the
orig
inal
fig
ure
is m
oved
the
sam
e di
stan
ce a
nd in
the
sam
edi
rect
ion.
To g
raph
a t
rans
latio
n of
a f
igur
e, m
ove
each
ver
tex
of t
he f
igur
e in
the
giv
en d
irect
ion.
The
nco
nnec
t th
e ne
w v
ertic
es.
y
xO
B' C
'
A'
A
B C
Ver
tice
s of
�A
BC
V
erti
ces
of �
AB
C(x
�5,
y�
2)
A(�
4,�
2)(�
4 �
5,�
2 �
2)
B(�
2,0)
(�2
�5,
0 �
2)
C(�
1,�
3)(�
1 �
5,�
3 �
2)
A(
1,0)
B(
3,2)
C(
4,�
1)
Exam
ple
Exer
cise
s
7MG
3.2
Answers (Lesson 10-9)
Chapter 10 A26 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Wor
d Pr
oble
m P
ract
ice
Tran
slat
ion
s
Cha
pter
10
61G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–9
pygp
10-9
MA
PSF
or E
xerc
ises
1–4
,use
th
e m
ap a
t th
e ri
ght.
Map
le S
t.
Blon
de S
t.
Dodg
e St
.
Paci
fic A
ve.
Cent
er R
d.
Harr
ison
St.
Kensington Ave.
Elmwood Ave.
Delaware Ave.
Main St.
New York Ave.
California Ave.
N
1.S
tan
ley’
s sc
hoo
l is
loc
ated
at
the
corn
erof
Cen
ter
and
Elm
woo
d.T
he
libr
ary
islo
cate
d at
th
e co
rner
of
Dod
ge a
nd
Del
awar
e.D
escr
ibe
Sta
nle
y’s
wal
k fr
omsc
hoo
l to
th
e li
brar
y as
an
ord
ered
pai
rof
th
e n
um
ber
of b
lock
s.(1
,2)
2.A
fter
he
goes
to
the
libr
ary,
Sta
nle
ygo
es t
o h
is A
un
t Je
ann
e’s
hou
se a
t th
eco
rner
of
Cal
ifor
nia
an
d H
arri
son
.D
escr
ibe
Sta
nle
y’s
wal
k fr
om t
he
libr
ary
to h
is a
un
t’s h
ouse
as
anor
dere
d pa
ir o
f th
e n
um
ber
of b
lock
s.(3
,�3)
3.If
a b
us
pick
s u
p pa
ssen
gers
at
the
corn
er o
f N
ew Y
ork
and
Map
le a
nd
driv
es 2
blo
cks
sou
th a
nd
3 bl
ocks
w
est,
wh
ere
does
th
e bu
s en
d u
p?th
e co
rner
of
Elm
wo
od
an
dD
od
ge
4.O
rgan
izer
s of
a w
alka
thon
wan
t to
map
out
a ro
ute
th
at w
ill
lead
peo
ple
from
the
corn
er o
f C
ente
r an
d K
ensi
ngt
on t
oth
e co
rner
of
Cal
ifor
nia
an
d M
aple
.W
rite
a c
oord
inat
e pa
ir t
hat
des
crib
esth
e m
ost
dire
ct r
oute
.(5
,4)
5.G
EOM
ETRY
Th
e fi
gure
sh
ows
anoc
tago
n p
lott
ed o
n a
coo
rdin
ate
syst
em.
Th
e fi
gure
is
to b
e tr
ansl
ated
by
5 u
nit
sle
ft a
nd
5 u
nit
s do
wn
.Gra
ph t
he
tran
slat
ed i
mag
e of
th
e fi
gure
.
y
xO
6.B
AN
KS
Cla
riss
a is
wai
tin
g in
lin
e at
th
e ba
nk.
Th
ere
are
seve
ral
peop
le i
nli
ne
in f
ron
t of
her
.Des
crib
e th
e pa
thC
lari
ssa
mu
st t
ake
to g
et t
o th
e fr
ont
of t
he
lin
e if
eac
h t
ime
she
mov
es u
p in
lin
e by
on
e po
siti
on i
s co
nsi
dere
d on
e u
nit
.
1 u
nit
rig
ht,
1 u
nit
up
,3 u
nit
s le
ft
telle
rs
Clar
issa
7MG
3.2
NA
ME
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____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice
Tran
slat
ion
s
Cha
pter
10
60G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-9
1.T
ran
slat
e re
ctan
gle
AB
CD
3 u
nit
s ri
ght
2.T
rian
gle
PQ
Ris
tra
nsl
ated
3
and
4 u
nit
s do
wn
.Gra
ph r
ecta
ngl
e u
nit
s le
ft a
nd
3 u
nit
s do
wn
.A
BC
D.
Th
en t
he
tran
slat
ed f
igu
re i
s tr
ansl
ated
6 u
nit
s ri
ght.
Gra
ph t
he
resu
ltin
g tr
ian
gle.
Tri
angl
e E
FG
has
ver
tice
s E
(1,1
),F
(4,�
3),a
nd
G(�
2,0)
.Fin
d t
he
vert
ices
of
E�F
�G�
afte
r ea
ch t
ran
slat
ion
.Th
en g
rap
h t
he
figu
rean
d i
ts t
ran
slat
ed i
mag
e.
3.3
un
its
left
,2 u
nit
s do
wn
4.4
un
its
up
E�(
�2,
�1)
,F�
(1,�
5),G
�(�
5,�
2)
E�(
1,5)
,F�(
4,1)
,G�(
�2,
4)
5.SE
ATS
Jati
n w
as g
iven
a n
ew s
eati
ng
assi
gnm
ent
in s
cien
ce c
lass
.Th
e di
agra
m s
how
s h
is o
ld s
eat
and
his
new
sea
t.D
escr
ibe
this
tra
nsl
atio
n i
n
wor
ds a
nd
as a
n o
rder
ed p
air.
3 u
nit
s ri
gh
t,2
un
its
do
wn
;(3
,�2)
REA
SON
ING
Th
e co
ord
inat
es o
f a
poi
nt
and
its
im
age
afte
r a
tran
slat
ion
are
giv
en.D
escr
ibe
the
tran
slat
ion
in
wor
ds
and
as
anor
der
ed p
air.
6.A
(1,�
2) →
A
(3,4
) 7.
H(3
,3) →
H
(�4,
0)8.
Z(�
2,�
4) →
Z(
1,�
5)2
un
its
rig
ht
and
7
un
its
left
an
d 3
3
un
its
rig
ht
and
16
un
its
up
;(2
,6)
un
its
do
wn
;(�
7,�
3)
un
it d
ow
n;
(3,�
1)
Fro
nt o
f Cla
ssro
om
OLD
NE
W
y
xO
E'
GG'
F' F
E
y
xO
E'
G
G'
F'
F
E
y
xO
Q'
P
P'
R'
RQ
y
xO
B'
C'
DA
CB
A'
D'
7MG
3.2
Answers (Lesson 10-9)
Chapter 10 A27 Glencoe California Mathematics, Grade 6
Exam
ple
NA
ME
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____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Spre
adsh
eet A
ctiv
ityTr
ansl
atio
ns
Cha
pter
10
63G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–9
pygp
10-9
You
can
use
a s
prea
dshe
et t
o de
term
ine
and
grap
h th
e or
dere
d pa
irs
of a
fig
ure
afte
r a
tran
slat
ion.
Qua
drila
tera
l AB
CD
has
the
vert
ices
A(2
,3),
B(�
1,2)
,C(�
2,�
3),
and
D(3
,�1)
.Use
a s
prea
dshe
et t
o fi
nd t
he v
erti
ces
of q
uadr
ilate
ral
A'B
'C'D
'aft
er a
tra
nsla
tion
4 u
nits
left
and
2 u
nits
up.
The
n us
e th
e sp
read
shee
t to
cr
eate
a g
raph
of
AB
CD
and
A'B
'C'D
'.
Step
1U
se C
olum
n A
for
the
x-co
ordi
nate
s an
d C
olum
n B
for
the
y-co
ordi
nate
s. E
nter
the
num
bers
usi
ng th
e fo
rmul
a ba
r. T
hen
pres
s EN
TER
to m
ove
to th
e ne
xt c
ell.
Be
sure
toen
ter
the
coor
dina
tes
of th
e fi
rst p
oint
aga
in a
t the
end
of
the
list
.
Step
2In
cel
l C1,
ent
er a
n eq
uals
sig
n fo
llow
ed b
y �
A1�
4. T
hen
pres
s EN
TER
to r
etur
n th
e x-
coor
dina
te o
f th
e ne
w p
oint
.
Step
3In
cel
l D1,
ent
er a
n eq
uals
sig
n fo
llow
ed b
y �
B1�
2. T
hen
pres
s EN
TER
to r
etur
n th
e y-
coor
dina
te o
f th
e ne
w p
oint
.
Step
4To
fin
d th
e re
mai
ning
new
x-c
oord
inat
es, c
lick
on
the
bott
om r
ight
cor
ner
of c
ell C
1an
ddr
ag it
to c
ell C
5. C
lick
on
the
bott
om r
ight
cor
ner
of c
ell D
1an
d dr
ag it
to c
ell D
5to
fin
dth
e y-
coor
dina
tes.
The
coo
rdin
ates
of
A'B
'C'D
'are
A'(�
2, 5
), B
'(�5,
4),
C'(�
6, �
1), a
nd D
'(�1,
1).
Step
5To
gra
ph, h
ighl
ight
col
umns
A a
nd B
thro
ugh
row
5. P
ress
the
Cha
rt W
izar
d. S
elec
t XY
(Sca
tter
) an
d ch
oose
the
grap
h w
ith
data
poi
nts
conn
ecte
d by
line
s. P
ress
NEX
T. S
elec
tth
e S
ER
IES
tab.
Pre
ss th
e AD
Dbu
tton
. In
the
X-V
alue
s ba
r, en
ter
�Sh
eet1
!$C$
1:$C
$5. I
nth
e Y-
Val
ues
bar,
ente
r �
Shee
t1!$
D$1:
$D$5
. Pre
ss N
EXT,
NEX
T, F
INIS
Hto
dis
play
the
grap
h.
Qua
drila
tera
l QU
AD
has
vert
ices
Q(�
2,1)
,U(2
,4),
A(3
,�3)
and
D(�
1,�
1).U
sea
spre
adsh
eet
to f
ind
the
vert
ices
of
Q'U
'A'D
'aft
er a
tran
slat
ion
of 2
uni
ts r
ight
and
3 un
its
dow
n.T
hen
use
asp
read
shee
t to
gra
ph Q
UA
Dan
d Q
'U'A
'D'.
Q(
0,-2
),U
(4,
1),A
(5,
-6)
D(
1,-4
)
AB
CD
EF
GH
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 -1 -2 3
3 2 -3 -1
-2 -5 -5 -1
5 4 -1 12
3-1
5
Sh
eet
1S
hee
t 2
Sh
eet
3
-8-6
-4-2
24
Serie
s 1
Serie
s 2
-4-3-2-10123456
NA
ME
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____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
10
62G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-9
Ch
ess
Mo
ves
In t
he
gam
e of
ch
ess,
a kn
igh
t ca
n m
ove
seve
ral
diff
eren
t w
ays.
It c
an m
ove
two
spac
es v
erti
call
y or
hor
izon
tall
y,th
en o
ne
spac
e at
a 9
0�an
gle.
It c
an a
lso
mov
e on
esp
ace
vert
ical
ly o
r h
oriz
onta
lly,
then
tw
osp
aces
at
a 90
�an
gle.
Sev
eral
exa
mpl
es
of a
kn
igh
t’s m
oves
are
in
dica
ted
on t
he
grid
at
the
righ
t.
1.U
se t
he
diag
ram
at
the
righ
t.P
lace
a k
nig
ht
or o
ther
pie
ce
in t
he
squ
are
mar
ked
1.M
ove
the
knig
ht
so t
hat
it
lan
ds o
n
each
of
the
rem
ain
ing
wh
ite
squ
ares
on
ly o
nce
.Mar
k ea
chsq
uar
e in
wh
ich
th
e kn
igh
t la
nds
wit
h 2
,th
en 3
,an
d so
on
.S
amp
le a
nsw
er g
iven
.Oth
er a
nsw
ers
are
po
ssib
le.
2.U
se t
he
diag
ram
bel
ow.P
lace
a k
nig
ht
or o
ther
pie
ce i
n t
he
squ
are
mar
ked
1.M
ove
the
knig
ht
so t
hat
it
lan
ds o
n e
ach
of
the
rem
ain
ing
squ
ares
on
ly o
nce
.Mar
k ea
ch s
quar
e in
wh
ich
th
e kn
igh
t la
nds
wit
h
2,th
en 3
,an
d so
on
.
Sam
ple
an
swer
giv
en.O
ther
answ
ers
are
po
ssib
le.
216
2717
187
22
2
15 12 3
4 23 16
8
3019
2813
2411
926
2510
514
2029 1
63
48
72
5
1
7MG
3.2
Answers (Lesson 10-9)
Chapter 10 A28 Glencoe California Mathematics, Grade 6
An
swer
s
Exer
cise
s
NA
ME
____
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____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Ref
lect
ion
s
Cha
pter
10
65G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–10
pygp
10-1
0
Det
erm
ine
wh
eth
er e
ach
fig
ure
has
lin
e sy
mm
etry
.If
so,d
raw
all
lin
es o
f sy
mm
etry
.n
o sy
mm
etry
Tri
angl
e D
EF
has
ver
tice
s D
(2,2
),E
(5,4
),an
d
F(1
,5).
Fin
d t
he
coor
din
ates
of
the
refl
ecte
dim
age.
Gra
ph
th
e fi
gure
an
d i
ts r
efle
cted
im
age
over
th
e x-
axis
.
Plo
t th
e ve
rtic
es a
nd
con
nec
t to
for
m �
DE
F.T
he
x-ax
is i
s th
e li
ne
of s
ymm
etry
.Th
e di
stan
ce f
rom
a p
oin
t on
�D
EF
to t
he
lin
e of
sym
met
ry i
s th
e sa
me
as t
he
dist
ance
fr
om t
he
lin
e of
sym
met
ry t
o th
e re
flec
ted
imag
e.T
he
imag
e co
ordi
nat
es a
re D
(2,
�2)
,E
(5,
�4)
,an
d F
(1,
�5)
.
For
Exe
rcis
es 1
an
d 2
,det
erm
ine
wh
ich
fig
ure
s h
ave
lin
e sy
mm
etry
.W
rite
yes
or n
o.If
yes
,dra
w a
ll l
ines
of
sym
met
ry.
1.2.
yes
no
3.
Tri
angl
e A
BC
has
ver
tice
s A
(0,4
),B
(2,1
),an
d C
(4,3
).F
ind
the
coor
din
ates
of
the
vert
ices
of
AB
Caf
ter
a re
flec
tion
ove
r th
e x-
axis
.Th
en g
raph
th
e fi
gure
an
d it
s re
flec
ted
imag
e.
A�(
0,�
4),B
�(2,
�1)
,an
d C
�(4,
�3)
y
xO
E'
D'D
F'
FE
A t
ype
of t
rans
form
atio
n w
here
a f
igur
e is
flip
ped
over
a li
ne o
f sy
mm
etry
is a
ref
lect
ion.T
o dr
aw t
here
flect
ion
of a
pol
ygon
, fin
d th
e di
stan
ce f
rom
eac
h ve
rtex
of
the
poly
gon
to t
he li
ne o
f sy
mm
etry
.Plo
tth
e ne
w v
ertic
es t
he s
ame
dist
ance
fro
m t
he li
ne o
f sy
mm
etry
but
on
the
othe
r si
de o
f th
e lin
e.T
hen
conn
ect
the
new
ver
tices
to
com
plet
e th
e re
flect
ed im
age.
Fig
ures
tha
t m
atch
exa
ctly
whe
n fo
lded
in h
alf
have
lin
e sy
mm
etry
.Eac
h fo
ld li
ne is
cal
led
a lin
e o
fsy
mm
etry
.Som
e fig
ures
hav
e m
ore
than
one
line
of
sym
met
ry.
y
xOA A'
BB
'
C C'
Exam
ple
s
Exam
ple
3
7MG
3.2
NA
ME
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____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Less
on R
eadi
ng G
uide
Ref
lect
ion
s
Cha
pter
10
64G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-1
0
Get
Rea
dy
for
the
Less
on
Com
ple
te t
he
Min
i L
ab a
t th
e to
p o
f p
age
558
in y
our
text
boo
k.W
rite
you
r an
swer
s b
elow
.
1.D
escr
ibe
how
you
dre
w t
he
refl
ecti
on o
f yo
ur
clas
smat
e’s
nam
e.S
ee s
tud
ents
’wo
rk.
2.E
xpla
in w
hy
the
lin
e w
her
e th
e ge
omir
ror
and
pape
r m
eet
is c
alle
d th
eli
ne
of s
ymm
etry
.S
amp
le a
nsw
er:T
he
fig
ure
s w
ritt
en o
n t
he
pap
er a
nd
ref
lect
ed t
hro
ug
h t
he
geo
mir
ror
are
mir
ror
imag
es.
Rea
d t
he
Less
on
3.Is
th
e im
age
of a
ref
lect
ion
sm
alle
r,la
rger
,or
the
sam
e si
ze a
s th
eor
igin
al f
igu
re?
sam
e si
ze
4.In
Exa
mpl
e 4
on p
age
559,
how
can
you
tel
l th
at o
ne
imag
e is
a r
efle
ctio
nof
th
e ot
her
acr
oss
the
x-ax
is?
Sam
ple
an
swer
:If
yo
u f
old
th
eg
rid
alo
ng
th
e x-
axis
,Can
d C
w
ill b
e o
n t
op
of
each
oth
er,
as w
ill b
e B
and
B
and
Aan
d A
.5.
Stu
dy t
he
coor
din
ates
giv
en i
n E
xam
ples
4 a
nd
5 on
pag
e 55
9.H
ow c
anyo
u t
ell
how
man
y u
nit
s a
vert
ex i
s aw
ay f
rom
th
e x-
axis
wit
hou
tgr
aph
ing
it?
How
can
you
tel
l h
ow m
any
un
its
a ve
rtex
is
away
fro
m t
he
y-ax
is?
Sam
ple
an
swer
:Th
e d
ista
nce
a p
oin
t is
aw
ay f
rom
the
x-ax
is is
th
e sa
me
as t
he
y-co
ord
inat
e o
f th
e p
oin
t;th
ed
ista
nce
a p
oin
t is
aw
ay f
rom
th
e y-
axis
is t
he
sam
e as
th
ex-
coo
rdin
ate
of
the
po
int.
Rem
emb
er W
hat
Yo
u L
earn
ed6.
Wor
k w
ith
a p
artn
er.D
raw
an
d cu
t ou
t fi
gure
s of
reg
ula
r po
lygo
ns.
Dem
onst
rate
wh
ich
reg
ula
r po
lygo
ns
hav
e li
nes
of
sym
met
ry a
nd
wh
ich
do n
ot.M
ark
the
lin
es o
f sy
mm
etry
wit
h d
ash
ed l
ines
on
th
e m
odel
s.S
ee s
tud
ents
’wo
rk.
7MG
3.2
Answers (Lesson 10-10)
Chapter 10 A29 Glencoe California Mathematics, Grade 6
Det
erm
ine
wh
eth
er e
ach
fig
ure
has
lin
e sy
mm
etry
.If
so,c
opy
the
figu
re a
nd
dra
w a
ll l
ines
of
sym
met
ry.
1.2.
3.
no
yes
no
4.5.
6.
yes
no
yes
7.G
raph
�A
BC
wit
h v
erti
ces
A(2
,2),
8.G
raph
squ
are
AB
CD
wit
h v
erti
ces
B(5
,4),
and
C(5
,1)
and
its
refl
ecti
on o
ver
A(�
1,2)
,B(2
,�1)
,C(5
,2),
and
D(2
,5)
the
x-ax
is.T
hen
fin
d th
e co
ordi
nat
esan
d it
s re
flec
tion
ove
r th
e y-
axis
.Th
enof
th
e re
flec
ted
imag
e.fi
nd
the
coor
din
ates
of
the
refl
ecte
d im
age.
A�(
2,�
2),B
�(5,
�4)
,C�(
5,�
1)A
�(1,
2),B
�(�
2,�
1),C
�(�
5,2)
,D
�(�
2,5)
Th
e co
ord
inat
es o
f a
poi
nt
and
its
im
age
afte
r a
refl
ecti
on a
re g
iven
.D
escr
ibe
the
refl
ecti
on a
s ov
er t
he
x-ax
is o
r y-
axis
.
9.B
(1,�
2) →
B(
1,2)
10
.J
(�3,
5) →
J(
�3,
�5)
11.
W(�
7,�
4) →
W(
7,�
4)x-
axis
x-ax
isy-
axis
y
xO
D' A
A'
C
D
B'
B
C'
y
xO
C'
A A'
CB B'
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice
Ref
lect
ion
s
Cha
pter
10
67G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–10
pygp
10-1
07M
G3.
2
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Skill
s Pr
actic
eR
efle
ctio
ns
Cha
pter
10
66G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-1
0
Det
erm
ine
wh
ich
fig
ure
s h
ave
lin
e sy
mm
etry
.Th
en d
raw
all
lin
es o
fsy
mm
etry
.
1.2.
3.
no
sym
met
ry
4.5.
6.
no
sym
met
ryG
rap
h t
he
figu
re a
nd
its
ref
lect
ion
ove
r th
e x-
axis
.Th
en f
ind
th
eco
ord
inat
es o
f th
e re
flec
ted
im
age.
7.tr
ian
gle
AB
Cw
ith
ver
tice
s A
(�3,
4),
B(1
,4),
and
C(3
,1)
A(
�3,
�4)
,B(
1,�
4),a
nd
C(
3,�
1)8.
rect
angl
e M
NO
Pw
ith
ve
rtic
es M
(�2,
�4)
,N
(�2,
�1)
,O(3
,�1)
,an
dP
(3,�
4)M
(�
2,4)
,N(
�2,
1),
O(
3,1)
,P(
3,4)
Gra
ph
th
e fi
gure
an
d i
ts r
efle
ctio
n o
ver
the
y-ax
is.T
hen
fin
d t
he
coor
din
ates
of
the
refl
ecte
d i
mag
e.
9.tr
ian
gle
DE
Fw
ith
ver
tice
s D
(1,4
),10
.tr
apez
oid
WX
YZ
wit
h v
erti
ces
W(�
1,3)
,E
(4,3
),an
d F
(2,0
)X
(�1,
�4)
,Y(�
5,�
4),a
nd
Z(�
3,3)
D(
�1,
4),E
(�
4,3)
,an
d F
(�
2,0)
W(
1,3)
,X(
1,�
4),Y
(5,
�4)
,Z(
3,3)
y
xO X
Z'
Y'
Y
ZW
W'
Z'
y
xO
FF
'
E'
ED
D'
y
xO
M'
N'
P'
O'
N M
O P
y
xO
A A'
B B'
C C'7M
G3.
2
Answers (Lesson 10-10)
Chapter 10 A30 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
10
69G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 10–10
pygp
10-1
0
The
Twel
ve D
ot
Puzz
leIn
th
is p
uzz
le,a
bro
ken
lin
e m
ade
up
of 5
seg
men
ts m
ust
pa
ss t
hro
ugh
eac
h o
f 12
dot
s.T
he
lin
e ca
nn
ot g
o th
rou
gh
a do
t m
ore
than
on
ce,a
lth
ough
it
may
in
ters
ect
itse
lf.T
he
lin
e m
ust
sta
rt a
t on
e do
t an
d en
d at
a d
iffe
ren
t do
t.
On
e so
luti
on t
o th
is p
uzz
le i
s sh
own
at
the
righ
t.T
wo
solu
tion
s to
th
e pu
zzle
are
not
“di
ffer
ent”
if o
ne
is ju
st
a re
flec
tion
or
rota
tion
of
the
oth
er.
Fin
d 1
8 ot
her
sol
uti
ons.
1.2.
3.
4.5.
6.
7.8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
7MG
3.2
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Wor
d Pr
oble
m P
ract
ice
Ref
lect
ion
s
Cha
pter
10
68G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-1
0
1.FL
AG
ST
he
figu
re s
how
s a
flag
sim
ilar
to t
he
nat
ion
al f
lag
of D
enm
ark.
How
man
y li
nes
of
sym
met
ry d
oes
the
flag
hav
e? D
raw
all
lin
es o
f sy
mm
etry
.
1
2.FL
AG
ST
he
figu
re s
how
s a
flag
sim
ilar
to t
he
nat
ion
al f
lag
of S
wit
zerl
and.
How
man
y li
nes
of
sym
met
ry d
oes
the
flag
hav
e? D
raw
all
lin
es o
f sy
mm
etry
.
4
3.IN
TER
IOR
DES
IGN
An
in
teri
or d
esig
ner
has
bee
n h
ired
to
deco
rate
a r
oom
th
ath
as t
he
shap
e of
a r
egu
lar
hex
agon
.B
efor
e be
gin
nin
g w
ork,
the
desi
gner
stu
dies
th
e sy
mm
etry
of
the
room
.How
man
y li
nes
of
sym
met
ry d
oes
the
room
hav
e? D
raw
all
lin
es o
f sy
mm
etry
on
the
figu
re.
6
4.A
STR
OLO
GY
Th
e fi
gure
sh
ows
the
astr
olog
ical
sym
bol
for
Sag
itta
riu
spl
otte
d on
a c
oord
inat
e sy
stem
.Ref
lect
the
sym
bol
acro
ss t
he
x-ax
is.G
raph
th
ere
flec
ted
imag
e.
y
xO
5.A
RC
HIT
ECTU
RE
A c
orpo
rate
pla
za i
s to
be b
uil
t ar
oun
d a
smal
l la
ke.B
uil
din
g 1
has
alr
eady
bee
n b
uil
t.S
upp
ose
ther
ear
e ax
es t
hro
ugh
th
e la
ke a
s sh
own
.S
how
wh
ere
Bu
ildi
ng
2 sh
ould
be
buil
tif
it
wil
l be
a r
efle
ctio
n o
f B
uil
din
g 1
acro
ss t
he
y-ax
is f
ollo
wed
by
are
flec
tion
acr
oss
the
x-ax
is.
y
xO
Build
ing
1
Lake
Build
ing
2
6.A
RC
HIT
ECTU
RE
Use
th
e in
form
atio
nfr
om E
xerc
ise
5.S
upp
ose
that
a t
hir
dbu
ildi
ng
is t
o be
bu
ilt
as s
how
n.T
oco
mpl
ete
the
busi
nes
s pa
rk,s
how
wh
ere
a fo
urt
h b
uil
din
g sh
ould
be
buil
tif
it
is a
ref
lect
ion
of
Bu
ildi
ng
3 ac
ross
the
x- a
nd
y-ax
is. y
xO
Build
ing
1Bu
ildin
g 3
Lake
Build
ing
2Bu
ildin
g 47M
G3.
2
Answers (Lesson 10-10)
Chapter 10 A31 Glencoe California Mathematics, Grade 6
Exer
cise
s
Exam
ple
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
TI-7
3 A
ctiv
ityL
ines
of
Sym
met
ry
Cha
pter
10
70G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10-1
0
Dra
w p
olyg
ons
on t
he c
alcu
lato
r by
ent
erin
g th
e co
ordi
nate
s of
the
ver
tice
s.U
se t
he D
RAW
feat
ure
to c
heck
for
ver
tica
l and
/or
hori
zont
al li
nes
of s
ymm
etry
.
The
ver
tice
s of
a p
olyg
on a
re:(
1,2)
,(7,
2),(
7,4)
,(4,
7),a
nd (
1,4)
.Dra
w t
hepo
lygo
n an
d te
ll w
heth
er it
has
ver
tica
l and
hor
izon
tal l
ines
of
sym
met
ry.
Step
1C
lear
all
list
s.
[MEM
] 6
Step
2E
nter
the
x-co
ordi
nate
s in
L1.
Ent
er th
e y-
coor
dina
tes
in L
2. R
epea
t the
fir
st v
alue
at t
heen
d of
eac
h co
lum
n.
Step
3C
reat
e Pl
ot1.
[PLO
T]4
[PLO
T]1
Step
4C
hoos
e L1
and
L2, i
f no
t alr
eady
cho
sen.
[STA
T][S
TAT]
Step
5S
et th
e gr
aph
win
dow
and
dis
play
the
plot
.
4
Step
6D
raw
a v
erti
cal l
ine
thro
ugh
the
poly
gon.
Use
the
arro
w k
eys
to c
ente
r th
e li
ne.
4
Thi
s po
lygo
n ha
s a
vert
ical
line
of
sym
met
ry.
Dra
w e
ach
pol
ygon
on
th
e ca
lcu
lato
r an
d f
ind
an
y ve
rtic
al o
r h
oriz
onta
l li
nes
of
sym
met
ry.
1.(1
, 5)
2.(1
0, 3
)(4
, 1)
(6, 6
)(4
, 9)
(2, 3
)h
ori
zon
tal l
ine
vert
ical
lin
e o
f sy
mm
etry
of
sym
met
ry
3.(5
, 3)
4.(2
, 6)
(1, 1
)(4
, 1)
(8, 1
)(7
, 1)
(12,
3)
(9, 6
)n
o li
ne
of
vert
ical
lin
e o
f sy
mm
etry
sym
met
ry
DR
AW
ZO
OM
EN
TE
R2n
dE
NT
ER
2nd
EN
TE
RE
NT
ER
2nd
EN
TE
R2n
d
LIS
T
EN
TE
R2n
d
Answers (Lesson 10-10)
Chapter 10 A32 Glencoe California Mathematics, Grade 6
Chapter 10 A33 Glencoe California Mathematics, Grade 6
Chapter 10 Assessment Answer KeyQuiz 1 (Lessons 10-1 and 10-3) Quiz 3 (Lessons 10-7 and 10-8) Mid-Chapter TestPage 73 Page 74 Page 75
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Quiz 2 (Lessons 10-5 and 10-6)
Page 73
Quiz 4 (Lessons 10-9 and 10-10)
Page 74
1.
2.
3.
4.
5.Not a polygon; it is
not closed.
hexagon; not regular
�23
� cm
3 ft
4 in.
1.
2.
3.
4.
5.A�(3, 2); B�(1, 4);
C�(1, �1); D�(3, �3)
y
xO
B'
A'
D'
C'C
B
A
D
(�10, �4)
yes
D�(1, 5); E�(5, 5);F�(6, 2); G�(�1, 3)
(�1, 1)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12. parallelogram
trapezoid
acute; equilateral
right; isosceles
neither
supplementary
rightobtuseacute
D
J
B1.
2.
3.
4.
5. adjacent
vertical
supplementary
complementary
sleeping
1.
2.
3.
4.
5. C
61
130
128°; obtuse
63°; acute
Chapter 10 Assessment Answer KeyVocabulary Test Form 1Page 76 Page 77 Page 78
Chapter 10 A34 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Sample answer: ameasurement found byusing similar triangles tofind a dimension that is toodifficult to measure directly
Sample answer: lines in aplane that, if extendedindefinitely, will neverintersect
three
measure
obtuse
reflection
tessellation
five
four
no
complementary
angles 1.
2.
3.
4.
5.
6.
7.
8.
9.
10. G
D
J
A
G
B
H
C
G
A 11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: decagon
F
A
H
A
G
D
H
C
F
B
Chapter 10 A35 Glencoe California Mathematics, Grade 6
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.Chapter 10 Assessment Answer Key
Form 2A Form 2BPage 79 Page 80 Page 81 Page 82
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 20-gon
H
A
G
A
G
D
H
C
G
A1.
2.
3.
4.
5.
6.
7.
8.
9.
10. H
D
G
B
F
B
F
C
F
D 1.
2.
3.
4.
5.
6.
7.
8.
9.
10. H
B
J
C
G
A
G
C
H
A 11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 16-gon
J
B
G
D
F
D
G
D
H
C
Chapter 10 A36 Glencoe California Mathematics, Grade 6
Chapter 10 Assessment Answer KeyForm 2CPage 83 Page 84
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. 83�
trapezoid
rectangle
90
117
82
8°
$1, 180�; $5, 30�;$10, 30�; $20, 120�;
Bills in Circulation
8%$5 Bills 8%
$10 Bills
50%$1 Bills
33%$20 Bills
�JKL, �LKJ,�K, �2; obtuse
�ABC, �CBA,�B, �1; acute
straight12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
No; 160 does not gointo 360 evenly.
Avery: fish; Nathan:pasta; Alex: tacos;Takara: salad
68°
x-axis
A(1, 2), B (�2, 3),C(0, �3); A�(5, 4),B�(2, 5), C�(4, �1)
135�
108�
8 ft
No; Sample answer:
�35
� � �12
�
y
x0C'
B' A'
C
BA
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Chapter 10 A37 Glencoe California Mathematics, Grade 6
An
swer
s
Chapter 10 Assessment Answer KeyForm 2DPage 85 Page 86
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. 45�
trapezoid
rhombus
90
63
44
110°
$5, 40�; $10, 40�;$20, 160�; $100, 120�
Bills in Circulation
33%$100 Bills
44%$20 Bills
11%$10 Bills
$5 Bills
11%
�QRS, �SRQ,�R, �4; acute
�FGH, �HGF, �G, �3;obtuse
right 12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
No; 135 does not gointo 360 evenly.
Avery: pasta;Nathan: fish;Alex: tacos;
Takara: salad
51°
y-axis
A�(�1, 5); B�(�4, 6);C�(�2, 0)
y
xOC'
B'
B
A'
A
C
140�
120�
5 cm
no; Sample answer:
�53
� � �31
�
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Chapter 10 A38 Glencoe California Mathematics, Grade 6
Chapter 10 Assessment Answer KeyForm 3Page 87 Page 88
1.
2.
3.
5.
6.
7.
8.
9.
10.
11. 70�
parallelogram
quadrilateral
111
53
14
71.5°
Bills in Circulation
36%$1 Bills
3%$2 Bills8%
$5 Bills7%$10 Bills
23%$20 Bills
5%$50 Bills
16%$100 Bills
�CDE, �EDC, �D�6; acute
�LMN, �NML,�M, �5; obtuse
obtuse
4.
$1, 130°; $2, 12°;$5, 31°; $10, 26°;$20, 83°; $50, 18°;$100, 59°
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
Yes; 120 goesinto 360 evenly.
Avery: gymnastics;Nathan: basketball;Alex: soccer;Takara: swimming
94.8�
W�(1, 2); X �(�3, 2);Y �(�1, �1); Z �(3, �1)
y
xOZ'Y'
W'X'
Y
X
Z
W
4 units left and 3 units up
160�
144�
6 ft
No; Sample answer:�65
� � �32
�
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Chapter 10 A39 Glencoe California Mathematics, Grade 6
An
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s
Chapter 10 Assessment Answer KeyPage 89, Extended-Response Test
Scoring Rubric
Level Specific Criteria
4 The student demonstrates a thorough understanding of the mathematicsconcepts and/or procedures embodied in the task. The student hasresponded correctly to the task, used mathematically sound procedures,and provided clear and complete explanations and interpretations. Theresponse may contain minor flaws that do not detract from thedemonstration of a thorough understanding.
3 The student demonstrates an understanding of the mathematics conceptsand/or procedures embodied in the task. The student’s response to thetask is essentially correct with the mathematical procedures used and theexplanations and interpretations provided demonstrating an essential butless than thorough understanding. The response may contain minor errorsthat reflect inattentive execution of the mathematical procedures orindications of some misunderstanding of the underlying mathematicsconcepts and/or procedures.
2 The student has demonstrated only a partial understanding of themathematics concepts and/or procedures embodied in the task. Althoughthe student may have used the correct approach to obtaining a solution ormay have provided a correct solution, the student’s work lacks an essentialunderstanding of the underlying mathematical concepts. The responsecontains errors related to misunderstanding important aspects of the task,misuse of mathematical procedures, or faulty interpretations of results.
1 The student has demonstrated a very limited understanding of themathematics concepts and/or procedures embodied in the task. Thestudent’s response to the task is incomplete and exhibits many flaws.Although the student has addressed some of the conditions of the task, thestudent reached an inadequate conclusion and/or provided reasoning thatwas faulty or incomplete. The response exhibits many errors or may beincomplete.
0 The student has provided a completely incorrect solution oruninterpretable response, or no response at all.
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Chapter 10 A40 Glencoe California Mathematics, Grade 6
Chapter 10 Assessment Answer Key Page 89, Extended-Response Test
Sample AnswersIn addition to the scoring rubric found on page A39, the following sample answers may be used as guidance in evaluating extended-response assessment items.
1. a.
The sides of a polygon are all linesegments with no curves. A polygonis simple and closed.
b. All triangles have two acute angles.Triangles are classified by theirthird angle.
See students’ triangles.
c. A rhombus is a quadrilateral thathas 4 congruent sides.
A square is a quadrilateral that has4 right angles and 4 congruent sides.
A rectangle is a quadrilateral thathas 4 right angles.
A trapezoid is a quadrilateral thathas only one pair of parallel sides.
See students’ quadrilaterals.
d. No. A trapezoid has exactly one setof parallel sides, and a rhombus hastwo sets of parallel sides.
e. A regular polygon has all sidescongruent and all angles congruent.
f. See students’ angles. Right anglesare 90�; obtuse angles are greaterthan 90� and less than 180�; straightangles are 180�, and acute angles aregreater than 0� and less than 90�.
g. The sum of two angles that aresupplementary is 180�. The sum oftwo angles that are complementaryis 90�, which is half the total forsupplementary angles, 180�.
See students’ drawings.
2. a. Octagons cannot fit together to coverspace because a third octagon cannotfit the 90� angle formed when 2octagons are placed together.
b.
See students’ explanations.
3. a. See students’ work.
b. See students’ work.
Chapter 10 A41 Glencoe California Mathematics, Grade 6
An
swer
s
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c.Chapter 10 Assessment Answer Key
Standardized Test PracticePage 90 Page 91
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D 11.
12.
13.
14.
15.
16.
17. A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
Chapter 10 A42 Glencoe California Mathematics, Grade 6
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Glencoe/M
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raw-H
ill Com
panies, Inc.Chapter 10 Assessment Answer Key
Standardized Test PracticePage 92
18.
19.
20.
21.
22.
23.
24.
25a.
25b.
25c. (�3, 5)
Translate the figure 3units left and 5 units up.
y
xO
X'
Y'
Z
Z'
XY
trapezoid
15
� ��
5.5 6.0 6.5 7.0 7.5 8.0 8.5
�� ��
$176.55
30
15.5%
7