chapter 7 resource masters - crunchymath.weebly.com · teacher’s guide to using the chapter 7...

Chapter 7Resource Masters

Consumable Workbooks Many of the worksheets contained in the Chapter ResourceMasters are available as consumable workbooks in both English and Spanish.

ISBN10 ISBN13

Study Guide and Intervention Workbook 0-07-877344-X 978-0-07-877344-0

Skills Practice Workbook 0-07-877346-6 978-0-07-877346-4

Practice Workbook 0-07-877347-4 978-0-07-877347-1

Word Problem Practice Workbook 0-07-877349-0 978-0-07-877349-5

Spanish Versions

Study Guide and Intervention Workbook 0-07-877345-8 978-0-07-877345-7

Practice Workbook 0-07-877348-2 978-0-07-877348-8

Answers for Workbooks The answers for Chapter 7 of these workbooks can be found in the back of this Chapter Resource Masters booklet.

StudentWorks PlusTM This CD-ROM includes the entire Student Edition test along withthe English workbooks listed above.

TeacherWorks PlusTM All of the materials found in this booklet are included for viewing,printing, and editing in this CD-ROM.

Spanish Assessment Masters (ISBN10: 0-07-877350-4, ISBN13: 978-0-07-877350-1)These masters contain a Spanish version of Chapter 7 Test Form 2A and Form 2C.

Copyright © by the McGraw-Hill Companies, Inc. All rights reserved. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe Geometry. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.

Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240

ISBN13: 978-0-07-873964-4ISBN10: 0-07-873964-0 Geometry CRM7

Printed in the United States of America

1 2 3 4 5 6 7 8 9 10 009 13 12 11 10 09 08 07 06

CONTENTS

Teacher’s Guide to Using the Chapter 7Resource Masters . . . . . . . . . . . . . . . . . . . . iv

Chapter ResourcesStudent-Built Glossary . . . . . . . . . . . . . . . . . . . 1Anticipation Guide (English) . . . . . . . . . . . . . . . 3Anticipation Guide (Spanish) . . . . . . . . . . . . . . 4

Lesson 7-1ProportionsLesson Reading Guide. . . . . . . . . . . . . . . . . . . 5Study Guide and Intervention . . . . . . . . . . . . . . 6Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . . 8Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Word Problem Practice . . . . . . . . . . . . . . . . . 10Enrichment. . . . . . . . . . . . . . . . . . . . . . . . . . . 11Graphing Calculator . . . . . . . . . . . . . . . . . . . . 12

Lesson 7-2Similar PolygonsLesson Reading Guide. . . . . . . . . . . . . . . . . . 13Study Guide and Intervention . . . . . . . . . . . . . 14Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 16Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Word Problem Practice . . . . . . . . . . . . . . . . . 18Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Lesson 7-3Similar TrianglesLesson Reading Guide. . . . . . . . . . . . . . . . . . 20Study Guide and Intervention . . . . . . . . . . . . . 21Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 23Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Word Problem Practice . . . . . . . . . . . . . . . . . 25Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Lesson 7-4Parallel Lines and Proportional PartsLesson Reading Guide. . . . . . . . . . . . . . . . . . 27Study Guide and Intervention . . . . . . . . . . . . . 28Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 30Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Word Problem Practice . . . . . . . . . . . . . . . . . 32Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Lesson 7-5Parts of Similar TrianglesLesson Reading Guide. . . . . . . . . . . . . . . . . . 34Study Guide and Intervention . . . . . . . . . . . . . 35Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 37Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38Word Problem Practice . . . . . . . . . . . . . . . . . 39Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 40Spreadsheet . . . . . . . . . . . . . . . . . . . . . . . . . 41

AssessmentStudent Recording Sheet . . . . . . . . . . . . . . . . 43Rubric for Pre-AP. . . . . . . . . . . . . . . . . . . . . . 44Chapter 7 Quizzes 1 and 2. . . . . . . . . . . . . . . 45Chapter 7 Quizzes 3 and 4. . . . . . . . . . . . . . . 46Chapter 7 Mid-Chapter Test . . . . . . . . . . . . . . 47Chapter 7 Vocabulary Test . . . . . . . . . . . . . . . 48Chapter 7 Test, Form 1 . . . . . . . . . . . . . . . . . 49Chapter 7 Test, Form 2A . . . . . . . . . . . . . . . . 51Chapter 7 Test, Form 2B . . . . . . . . . . . . . . . . 53Chapter 7 Test, Form 2C . . . . . . . . . . . . . . . . 55Chapter 7 Test, Form 2D . . . . . . . . . . . . . . . . 57Chapter 7 Test, Form 3 . . . . . . . . . . . . . . . . . 59Chapter 7 Extended-Response Test . . . . . . . . 61Standardized Test Practice. . . . . . . . . . . . . . . 62

Answers . . . . . . . . . . . . . . . . . . . . . . .A1–A29

iii

Teacher’s Guide to Using theChapter 7 Resource Masters

The Chapter 7 Resource Masters includes the core materials needed for Chapter 7.These materials include worksheets, extensions, and assessment options. Theanswers for these pages appear at the back of this booklet.

All of the materials found in this booklet are included for viewing and printing onthe TeacherWorks PlusTM CD-ROM.

Chapter ResourcesStudent-Built Glossary (pages 1–2)These masters are a student study tool that presents up to twenty of the keyvocabulary terms from the chapter.Students are to recording definitions and/orexamples for each term. You may suggestthat student highlight or star the termswith which they are not familiar. Give tostudents before beginning Lesson 7-1.Encourage them to add these pages to theirmathematics study notebooks. Remindthem to complete the appropriate words asthey study each lesson.

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 Thesemasters provide vocabulary, key concepts,additional worked-out examples and Check Your 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.

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,or widen students’ perspectives on themathematics they are learning. They arewritten for use with all levels of students.

iv

Graphing Calculator, ScientificCalculator, or Spreadsheet ActivitiesThese activities present ways in whichtechnology can be used with the concepts in some lessons of this chapter. Use as analternative approach to some concepts or as an integral part of your lessonpresentation.

Assessment OptionsThe assessment masters in the Chapter 7Resource 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 withbelow grade level students.

• Forms 2A and 2B contain multiple-choice questions aimed at on grade levelstudents. These tests are similar informat to offer comparable testingsituations.

• Forms 2C and 2D contain free-responsequestions aimed at on grade levelstudents. These tests are similar informat to offer comparable testingsituations.

• Form 3 is a free-response test for usewith above 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 forthe assessment masters.

v

Chapter 7 1 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Student-Built GlossaryNAME ______________________________________________ DATE ____________ PERIOD _____

7

Ch

apte

r R

eso

urc

esThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 7.As you study the chapter, complete each term’s definition or description. Rememberto add the page number where you found the term. Add these pages to yourGeometry Study Notebook to review vocabulary at the end of the chapter.

Vocabulary Term Found on Page Definition/Description/Example

cross products

extremes

means

midsegment

(continued on the next page)


Student-Built Glossary (continued)

NAME ______________________________________________ DATE ____________ PERIOD _____

7C

opyright ©G

lencoe/McG

raw-H

ill, a division of The M

cGraw

-Hill C

ompanies, Inc.

Vocabulary Term Found on Page Definition/Description/Example

proportion

ratio

scale factor

similar polygons


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Anticipation GuideProportions and Similarity

NAME ______________________________________________ DATE ____________ PERIOD _____

7

Before you begin Chapter 7

• 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 ordisagree, write NS (Not Sure).

After you complete Chapter 7

• 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 anexample of why you disagree.

STEP 1

STEP 2

STEP 1 Statement STEP 2A, D, or NS A or D

1. Ratios are always written as fractions.

2. A proportion is an equation stating that two ratios are equal.

3. Two ratios are in proportion to each other only if their cross products are equal.

4. If �ab� � �d

c�, then �

ac� � �

db�.

5. The ratio of the lengths of the sides of similar figures is called the scale factor for the two figures.

6. If one angle in a triangle is congruent to an angle in another triangle, then the two triangles are similar.

7. If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then the line separates the two sides into congruent segments.

8. A segment whose endpoints are the midpoints of two sides of a triangle is parallel to the third side of the triangle.

9. If two triangles are similar then their perimeters are equal.

10. The medians of two similar triangles are in the same proportion as corresponding sides.

Ch

apte

r R

eso

urc

es

Capítulo 7 4 Geometría de Glencoe

Ejercicios preparatoriosProporciones y semejanzas

NOMBRE ____________________________________________ FECHA ____________ PERÍODO _____

7C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

Antes de comenzar el Capítulo 7

• 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 7

• 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 2

PASO 1 Enunciado PASO 2A, D o NS A o D

1. Las razones se escriben siempre como fracciones.

2. Una proporción es una ecuación que establece que dos razones son iguales.

3. Dos razones son proporcionales entre sí sólo si sus productos cruzados son iguales.

4. Si �ab� � �d

c�, entonces �

ac� � �

db�.

5. La razón de las longitudes de los lados de figuras semejantes se llama factor de escala para las dos figuras.

6. Si un ángulo de un triángulo es congruente a un ángulo de otro triángulo, entonces los dos triángulos son semejantes.

7. Si una recta es paralela a un lado del triángulo e interseca los otros dos lados en dos puntos diferentes, entonces la recta separa los dos lados en segmentos congruentes.

8. Un segmento cuyos extremos son los puntos medios de dos lados de un triángulo es paralelo al tercer lado del triángulo.

9. Si dos triángulos son semejantes, éstos tienen el mismo perímetro.

10. Las medianas de dos triángulos semejantes están en la misma proporción que los lados correspondientes.


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Lesson Reading GuideProportions

NAME ______________________________________________ DATE ____________ PERIOD _____

7-1

Get Ready for the LessonRead the introduction to Lesson 7-1 in your textbook.

Estimate the ratio of length to width for the background rectangles in Tiffany’sClematis Skylight.

Read the Lesson

1. Match each description in the first column with a word or phrase from the secondcolumn.

a. The ratio of two corresponding quantities i. proportion

b. r and u in the equation �rs� � �u

t� ii. cross products

c. a comparison of two quantities iii. means

d. ru and st in the equation �rs� � �u

t� iv. scale factor

e. an equation stating that two ratios are equal v. extremes

f. s and t in the equation �rs� � �u

t� vi. ratio

2. If m, n, p, and q are nonzero numbers such that �mn� � �

pq�, which of the following

statements could be false?

A. np � mq B. �np

� � �mq�

C. mp � nq D. qm � pn

E. �mn� � �p

q� F. �p

q� � �m

n�

G. m:p � n:q H. m:n � p:q

3. Write two proportions that match each description.

a. Means are 5 and 8; extremes are 4 and 10.

b. Means are 5 and 4; extremes are positive integers that are different from means.

Remember What You Learned

4. Sometimes it is easier to remember a mathematical idea if you put it into words withoutusing any mathematical symbols. How can you use this approach to remember theconcept of equality of cross products?

Less

on

7-1

05-42 Geo-07-873964 4/12/06 8:44 PM Page 5


Study Guide and InterventionProportions

NAME ______________________________________________ DATE ____________ PERIOD _____

7-1C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

Write Ratios A ratio is a comparison of two quantities. The ratio a to b, where b is not zero, can be written as �

ab� or a:b. The ratio of two quantities is sometimes called a scale

factor. For a scale factor, the units for each quantity are the same.

In 2002, the Chicago Cubs baseball team won 67 games out of 162.Write a ratio for the number of games won to the total number of games played.To find the ratio, divide the number of games won by the total number of games played. The

result is �16672�, which is about 0.41. The Chicago Cubs won about 41% of their games in 2002.

A doll house that is 15 inches tall is a scale model of a real housewith a height of 20 feet. What is the ratio of the height of the doll house to theheight of the real house?To start, convert the height of the real house to inches.20 feet � 12 inches per foot � 240 inchesTo find the ratio or scale factor of the heights, divide the height of the doll house by theheight of the real house. The ratio is 15 inches:240 inches or 1:16. The height of the doll

house is �116� the height of the real house.

1. In the 2005 Major League baseball season, Alex Rodriquez hit 48 home runs and was at bat 605 times. Find the ratio of home runs to the number of times he was at bat.

2. There are 182 girls in the sophomore class of 305 students. Find the ratio of girls to total students.

3. The length of a rectangle is 8 inches and its width is 5 inches. Find the ratio of length to width.

4. The sides of a triangle are 3 inches, 4 inches, and 5 inches. Find the scale factor betweenthe longest and the shortest sides.

5. The length of a model train is 18 inches. It is a scale model of a train that is 48 feet long.Find the scale factor.

Example 1

Example 2

Exercises

05-42 Geo-07-873964 4/12/06 8:44 PM Page 6


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Study Guide and Intervention (continued)

Proportions

NAME ______________________________________________ DATE ____________ PERIOD _____

7-1

Use Properties of Proportions A statement that two ratios are equal is called aproportion. In the proportion �

ab� � �d

c�, where b and d are not zero, the values a and d are

the extremes and the values b and c are the means. In a proportion, the product of themeans is equal to the product of the extremes, so ad � bc.

�ab� � �d

c�

a � d � b � c↑ ↑

extremes means

Solve �196� � �

2x7�.

�196� � �

2x7�

9 � x � 16 � 27 Cross products

9x � 432 Multiply.

x � 48 Divide each side by 9.

A room is 49 centimeters by 28 centimeters on a scale drawing of a house. For the actual room, the larger dimension is 14 feet.Find the shorter dimension of the actual room.If x is the room’s shorter dimension, then

�2489� � �1

x4�

49x � 392 Cross products

x � 8 Divide each side by 49.

The shorter side of the room is 8 feet.

Solve each proportion.

1. �12� � �

2x8� 2. �

38� � �2

y4� 3. �

xx

��

222

� � �3100�

4. �183.2� � �

9y� 5. �

2x8� 3� � �

54� 6. �

xx

��

11� � �

34�

Use a proportion to solve each problem.

7. If 3 cassettes cost $44.85, find the cost of one cassette.

8. The ratio of the sides of a triangle are 8:15:17. If the perimeter of the triangle is 480 inches, find the length of each side of the triangle.

9. The scale on a map indicates that one inch equals 4 miles. If two towns are 3.5 inchesapart on the map, what is the actual distance between the towns?

shorter dimension��longer dimension

Example 1

Example 2

Exercises

Less

on

7-1

05-42 Geo-07-873964 4/12/06 8:44 PM Page 7


Skills PracticeProportions

NAME ______________________________________________ DATE ____________ PERIOD _____

7-1C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

1. FOOTBALL A tight end scored 6 touchdowns in 14 games. Find the ratio of touchdownsper game.

2. EDUCATION In a schedule of 6 classes, Marta has 2 elective classes. What is the ratioof elective to non-elective classes in Marta’s schedule?

3. BIOLOGY Out of 274 listed species of birds in the United States, 78 species made theendangered list. Find the ratio of endangered species of birds to listed species in theUnited States.

4. ART An artist in Portland, Oregon, makes bronze sculptures of dogs. The ratio of theheight of a sculpture to the actual height of the dog is 2:3. If the height of the sculptureis 14 inches, find the height of the dog.

5. SCHOOL The ratio of male students to female students in the drama club at CampbellHigh School is 3:4. If the number of male students in the club is 18, what is the numberof female students?


6. �25� � �4

x0� 7. �1

70� � �

2x1� 8. �

250� � �

46x�

9. �54x� � �

385� 10. �

x �3

1� � �

72� 11. �

135� � �

x �5

3�

Find the measures of the sides of each triangle.

12. The ratio of the measures of the sides of a triangle is 3:5:7, and its perimeter is 450 centimeters.

13. The ratio of the measures of the sides of a triangle is 5:6:9, and its perimeter is 220 meters.

14. The ratio of the measures of the sides of a triangle is 4:6:8, and its perimeter is 126 feet.

15. The ratio of the measures of the sides of a triangle is 5:7:8, and its perimeter is 40 inches.

05-42 Geo-07-873964 4/12/06 8:44 PM Page 8


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

PracticeProportions

NAME ______________________________________________ DATE ____________ PERIOD _____

7-1

1. NUTRITION One ounce of cheddar cheese contains 9 grams of fat. Six of the grams of fatare saturated fats. Find the ratio of saturated fats to total fat in an ounce of cheese.

2. FARMING The ratio of goats to sheep at a university research farm is 4:7.The number of sheep at the farm is 28. What is the number of goats?

3. ART Edward Hopper’s oil on canvas painting Nighthawks has a length of 60 inches and a width of 30 inches. A print of the original has a length of 2.5 inches. What is the width of the print?


4. �58� � �1

x2� 5. �1.

x12� � �

15� 6. �2

67x� � �

43�

7. �x �

32

� � �89� 8. �

3x4� 5� � �

�75� 9. �

x �4

2� � �

x �2

4�

Find the measures of the sides of each triangle.

10. The ratio of the measures of the sides of a triangle is 3:4:6, and its perimeter is 104 feet.

11. The ratio of the measures of the sides of a triangle is 7:9:12, and its perimeter is 84 inches.

12. The ratio of the measures of the sides of a triangle is 6:7:9, and its perimeter is 77 centimeters.

Find the measures of the angles in each triangle.

13. The ratio of the measures of the angles is 4:5:6.

14. The ratio of the measures of the angles is 5:7:8.

15. BRIDGES The span of the Benjamin Franklin suspension bridge in Philadelphia,Pennsylvania, is 1750 feet. A model of the bridge has a span of 42 inches. What is theratio of the span of the model to the span of the actual Benjamin Franklin Bridge?

Less

on

7-1

05-42 Geo-07-873964 4/12/06 8:44 PM Page 9

1. MODELS Luke wants to make a scalemodel of a Boeing 747 jetliner. He wantsevery foot of his model to represent 50feet. Complete the following table.

(Source: www.boeing.com)

2. RATIONS Sixteen students went on a week-long hiking trip. They broughtwith them 320 specially baked, protein-rich, cookies. What is the ratio of cookiesto students?

3. PHOTOGRAPHS Tracy is 4 feet tall and her father is 6 feet tall. In a photograph of the two of themstanding side by side, Tracy’s image is 2 inches tall.

Although their images are much smaller,the ratio of their heights remains thesame. How tall is Tracy’s father’s imagein the photo?

4. CARS A car company builds twoversions of one of its models—a sedanand a station wagon. The ratio of sedansto station wagons is 11 : 2. A freighterbegins unloading the cars at a dock.Tom counts 18 station wagons and thenoverhears a dock worker call out, “Okay,that’s all of the wagons . . . bring out the sedans!” How many sedans were onthe ship?

MAPS For Exercises 5–7, use thefollowing information.Carlos makes a map of his neighborhood for a presentation. The scale of his map is 1 inch : 125 feet.

5. How many feet do 4 inches represent onthe map?

6. Carlos lives 250 feet away from Andrew.How many inches separate Carlos’ homefrom Andrew’s on the map?

7. During a practice run in front of hisparents, Carlos realizes that his map is far too small. He decides to make his map 5 times as large. What would be the scale of the larger map?

6 ft4 ft


Word Problem PracticeProportions

NAME ______________________________________________ DATE ____________ PERIOD _____

7-1C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

Actual ModelPart length (in.) length (in.)

Wing Span 2,537

Length 2,782

Tail Height 392 7.84

05-42 Geo-07-873964 4/12/06 8:44 PM Page 10


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

EnrichmentNAME ______________________________________________ DATE ____________ PERIOD _____

7-1

Growth ChartsIt is said that when a child has reached the age of 2 years, he is roughly half of hisadult height. The growth chart below shows the growth according to percentiles forboys.

1. Use the chart to determine the approximate height for a boy at age 2 if he is inthe 75th to 95th percentile.

2. Using the rule that the height at age 2 is approximately half of his adult height,set up a proportion to solve for the adult height of the boy in exercise 1. Solveyour proportion.

3. Use the chart to approximate the height at age 18 for a boy if he is in the 75thto 95th percentile. How does this answer compare to the answer to problem 1?

4. Repeat this process for a boy who is in the 5th to 25th percentile.

5. Is using the rule that a boy is half of his adult height at age 2 years a goodapproximation? Explain.

85

75

65

55

45

35

2 4 6 8 10 12 14 16 18

Age (yr)

Hei

gh

t (i

n.)

Percentile Group

5th to 25th

25th to 75th

75th to 95th

A

B Less

on

7-1

05-42 Geo-07-873964 4/12/06 8:44 PM Page 11


Graphing Calculator ActivitySolving Proportions

NAME ______________________________________________ DATE ____________ PERIOD _____

7-1C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

You can use a calculator to solve proportions.

Solve the proportion by using cross products.

�5156..69

� � �45

x.8�

Multiply 16.9 by 45.8. Divide the product by 55.6.

Enter: 16.9 45.8 55.6 13.92122302

The solution is approximately 13.921.

Solve each proportion by using cross products. Round your answers to the nearest hundredth.

1. �1339..98

� � �10

x.5� 2. �

2357..97

� � �24

x.3� 3. �

1594..63

� � �27

x.7�

4. �6463..84

� � �16

x.9� 5. �

7357..42

� � �32

x.4� 6. �

46x.2� � �

2396..74

�

7. �14

x.9� � �

1264..86

� 8. �35

x.8� � �

3227..98

� 9. �46

x.9� � �

1959..79

�

10. �3241..91

� � �36

x.6� 11. �

99x.8� � �

3425..23� 12. �

68x.9� � �

4846..34

�

ENTER��

Example

05-42 Geo-07-873964 4/12/06 8:44 PM Page 12


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Lesson Reading GuideSimilar Polygons

NAME ______________________________________________ DATE ____________ PERIOD _____

7-2

Get Ready for the LessonRead the introduction to Lesson 7-2 in your textbook.• Describe the figures that have similar shapes.

• What happens to the figures as your eyes move from the center to the outer edge?

Read the Lesson1. Complete each sentence.

a. Two polygons that have exactly the same shape, but not necessarily the same size,are .

b. Two polygons are congruent if they have exactly the same shape and the same .

c. Two polygons are similar if their corresponding angles are and their corresponding sides are .

d. Two polygons are congruent if their corresponding angles are and their corresponding sides are .

e. The ratio of the lengths of corresponding sides of two similar figures is called the .

f. Multiplying the coordinates of all points of a figure in the coordinate plane by a scale factor to get a similar figure is called a .

g. If two polygons are similar with a scale factor of 1, then the polygons are .

2. Determine whether each statement is always, sometimes, or never true.a. Two similar triangles are congruent.b. Two equilateral triangles are congruent.c. An equilateral triangle is similar to a scalene triangle.d. Two rectangles are similar.e. Two isosceles right triangles are congruent.f. Two isosceles right triangles are similar.g. A square is similar to an equilateral triangle.h. Two acute triangles are similar.i. Two rectangles in which the length is twice the width are similar.j. Two congruent polygons are similar.

Remember What You Learned3. A good way to remember a new mathematical vocabulary term is to relate it to words

used in everyday life. The word scale has many meanings in English. Give three phrasesthat include the word scale in a way that is related to proportions.

Less

on

7-2

05-42 Geo-07-873964 4/12/06 8:44 PM Page 13


Study Guide and InterventionSimilar Polygons

NAME ______________________________________________ DATE ____________ PERIOD _____

7-2C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

Identify Similar Figures

Determine whether the triangles are similar.Two polygons are similar if and only if their corresponding angles are congruent and their corresponding sides are proportional.

�C � �Z because they are right angles, and �B � �X.By the Third Angle Theorem, �A � �Y.

For the sides, �BX

CZ� � �

2203�, �

BX

AY� � � �

2203�, and �

AY

CZ� � �

2203�.

The side lengths are proportional. So �BCA � �XZY.

Is polygon WXYZ � polygon PQRS?

For the sides, �WPQ

X� � �

182� � �

32�, �Q

XYR� � �

1182� � �

32�, �R

YZS� � �

1150� � �

32�,

and �ZSWP� � �

96� � �

32�. So corresponding sides are proportional.

Also, �W � �P, �X � �Q, �Y � �R, and �Z � �S, so corresponding angles are congruent. We can conclude that polygon WXYZ � polygon PQRS.

Determine whether each pair of figures is similar. If they are similar, give theratio of corresponding sides.

1. 2.

3. 4. 10y

8y

37�

37�116�

27�

5x

4x

15z12z

22

11

1610

equilateral triangles

15

9

12

18

XW

Z Y10

6

8

12

QP

S R

20�2��23�2�

20 23

2320 20��2 23��245�

45�C A X Z

B YExample 1

Example 2

Exercises

05-42 Geo-07-873964 4/12/06 8:44 PM Page 14


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.


Similar Polygons

NAME ______________________________________________ DATE ____________ PERIOD _____

7-2

Scale Factors When two polygons are similar, the ratio of the lengths of corresponding sides is called the scale factor. At the right, �ABC � �XYZ. The scale factor of �ABC to �XYZ is 2 and the scale factor of

�XYZ to �ABC is �12�.

3 cm

6 cm

8 cm

10 cm5 cm4 cm

Z

Y

XC

A

B

The two polygons aresimilar. Find x and y.

Use the congruent angles to write thecorresponding vertices in order.�RST � �MNPWrite proportions to find x and y.

�3126� � �1

x3� �

3y8� � �

3126�

16x � 32(13) 32y � 38(16)x � 26 y � 19

x

y38

3216 13

T

S

R P

N

M

�ABC � �CDE. Find the scale factor and find the lengths of C�D�and D�E�.

AC � 3 � 0 � 3 and CE � 9 � 3 � 6. Thescale factor of �CDE to �ABC is 6:3 or 2:1.Using the Distance Formula,AB � �1 � 9� � �10� and BC � �4 � 9� � �13�. The lengths of thesides of �CDE are twice those of �ABC,so DC � 2(BA) or 2�10� and DE � 2(BC) or 2�13�.

x

y

A(0, 0)

B(1, 3)

C(3, 0)

E(9, 0)

D

Each pair of polygons is similar. Find x and y.

1. 2.

3. 4.

5. In Example 2 above, point D has coordinates (5, 6). Use the Distance Formula to verifythe lengths of C�D� and D�E�.

40

36x

30

18 y12

y � 1

18

24

x18

10

y

4.5x

2.5

5

9

12

y8

10x

Example 1 Example 2

Exercises

Less

on

7-2

05-42 Geo-07-873964 4/12/06 8:44 PM Page 15


Skills PracticeSimilar Polygons

NAME ______________________________________________ DATE ____________ PERIOD _____

7-2C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

Determine whether each pair of figures is similar. Justify your answer.

1. 2.

Each pair of polygons is similar. Write a similarity statement, and find x, themeasure(s) of the indicated side(s), and the scale factor.

3. G�H� 4. S�T� and S�U�

5. W�T� 6. T�S� and S�P�

10

8

x � 2

x � 1

SP

M N

L

T

9

103

x � 1

5

P

S

RU V

WT

Q

x � 5

x � 5

9

3

44 S

W

XY

T

U26

14

12 13

B C

DA

13

76 x

G

E H

F

7.5

7.5

7.57.5

Z Y

XW

3

3

33S R

QP

10.5

6 9

59� 35�A C

B

7

4 659� 35�D F

E

05-42 Geo-07-873964 4/12/06 8:44 PM Page 16


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

PracticeSimilar Polygons

NAME ______________________________________________ DATE ____________ PERIOD _____

7-2

Determine whether each pair of figures is similar. Justify your answer.

1. 2.

Each pair of polygons is similar. Write a similarity statement, and find x, themeasure(s) of the indicated side(s), and the scale factor.

3. L�M� and M�N� 4. D�E� and D�F�

5. COORDINATE GEOMETRY Triangle ABC has vertices A(0, 0), B(�4, 0), and C(�2, 4).The coordinates of each vertex are multiplied by 3 to create �AEF. Show that �AEF issimilar to �ABC.

6. INTERIOR DESIGN Graham used the scale drawing of his living room to decide where to place furniture. Find the dimensions of theliving room if the scale in the drawing is 1 inch � 4.5 feet.

4 in.

21–2 in.

6 12

40�

40�

x � 1

x � 3AF

E

D

B C14

10

x � 6

x � 9

C N MD

A B LP

2412

14 162118

VUAC

B T

25 12

9

14.4

1524

20

15

JM Q R

SP

KL

Less

on

7-2

05-42 Geo-07-873964 4/12/06 8:44 PM Page 17


Word Problem PracticeSimilar Polygons

NAME ______________________________________________ DATE ____________ PERIOD _____

7-2C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

1. PANELS When closed, an entertainmentcenter is made of four square panels.The three smaller panels are congruentsquares.

What is the scale factor of the largersquare to one of the smaller squares?

2. DOWNSPOUTS During a storm, one of the downspouts on Mr. Herrera’shouse was broken and needed to bereplaced. Unfortunately, the downspoutwas too damaged to measure its lengthand it was too difficult to measure theheight of the gutter. Luckily, Mr. Herrerahad a scale model of his house. If the downspout in the model was 1�

12� feet

long and the scale factor was 20, howlong was the actual downspout?

3. ORIGAMI Baxter uses an 8-inch square piece of origami paper to makean origami model of a chicken. Whenfinished, the chicken stands 4 incheshigh. Baxter wants to make anotherorigami chicken, only this time he wants to make it 12 inches high instead.What size piece of paper should he useto do this?

4. ENLARGING Camille wants to make a pattern for a four-pointed star withdimensions twice as long as the oneshown. Help her by drawing a star withdimensions twice as long on the gridbelow.

BIOLOGY For Exercises 5–7, use thefollowing information.A paramecium is a small single-cellorganism. The paramecium magnified belowis actually one tenth of a millimeter long.

5. If you want to make a photograph of theoriginal paramecium so that its image is1 centimeter long, by what scale factorshould you magnify it?

6. If you want to make a photograph of theoriginal paramecium so that its image is15 centimeters long, by what scale factorshould you magnify it?

7. By approximately what scale factor hasthe paramecium been enlarged to makethe image shown?

05-42 Geo-07-873964 4/12/06 8:44 PM Page 18


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.


7-2

Constructing Similar PolygonsHere are four steps for constructing a polygon that is similar to and with sides twice as long as those of an existing polygon.

Step 1 Choose any point either inside or outside the polygon and label it O.Step 2 Draw rays from O through each vertex of the polygon.Step 3 For vertex V, set the compass to length OV. Then locate a new point

V� on ray OV such that VV� � OV. Thus, OV� � 2(OV ).Step 4 Repeat Step 3 for each vertex. Connect points V�, W�, X� and Y� to

form the new polygon.

Two constructions of polygons similar to and with sides twice those of VWXYare shown below. Notice that the placement of point O does not affect the sizeor shape of V�W�X�Y�, only its location.

Trace each polygon. Then construct a similar polygon with sides twice as long asthose of the given polygon.

1. 2. D E F

GC

A

B

VW

Y X

VW

Y X

V�

W�

X�Y�

O

VW

YX

V�

W�

X�Y�

O

3. Explain how to construct a similarpolygon with sides three times the lengthof those of polygon HIJKL. Then do theconstruction.

4. Explain how to construct a similar

polygon 1�12� times the length of those of

polygon MNPQRS. Then do theconstruction.

M

S

R

N

Q

P

H I

LK

J

Less

on

7-2

05-42 Geo-07-873964 4/12/06 8:44 PM Page 19


Lesson Reading GuideSimilar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

7-3C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

Get Ready for the LessonRead the introduction to Lesson 7-3 in your textbook.• What does it mean to say that triangular shapes result in rigid construction?

• What would happen if the shapes used in the construction were quadrilaterals?

Read the Lesson1. State whether each condition guarantees that two triangles are congruent or similar.

If the condition guarantees that the triangles are both similar and congruent, writecongruent. If there is not enough information to guarantee that the triangles will becongruent or similar, write neither.a. Two sides and the included angle of one triangle are congruent to two sides and the

included angle of the other triangle.b. The measures of all three pairs of corresponding sides are proportional.c. Two angles of one triangle are congruent to two angles of the other triangle.d. Two angles and a nonincluded side of one triangle are congruent to two angles and

the corresponding nonincluded side of the other triangle.e. The measures of two sides of a triangle are proportional to the measures of two

corresponding sides of another triangle, and the included angles are congruent.

f. The three sides of one triangle are congruent to the three sides of the other triangle.

g. The three angles of one triangle are congruent to the three angles of the other triangle.

h. One acute angle of a right triangle is congruent to one acute angle of another righttriangle.

i. The measures of two sides of a triangle are proportional to the measures of two sidesof another triangle.

2. Identify each of the following as an example of a reflexive, symmetric, or transitive property.a. If �RST � �UVW, then �UVW � �RST.b. If �RST � �UVW and �UVW � �OPQ, then �RST � �OPQ.c. �RST � �RST

Remember What You Learned3. A good way to remember something is to explain it to someone else. Suppose one of your

classmates is having trouble understanding the difference between SAS for congruenttriangles and SAS for similar triangles. How can you explain the difference to him?

05-42 Geo-07-873964 4/12/06 8:44 PM Page 20


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Study Guide and InterventionSimilar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

7-3

Identify Similar Triangles Here are three ways to show that two triangles are similar.

AA Similarity Two angles of one triangle are congruent to two angles of another triangle.

SSS Similarity The measures of the corresponding sides of two triangles are proportional.

SAS SimilarityThe measures of two sides of one triangle are proportional to the measures of two corresponding sides of another triangle, and the included angles are congruent.

Determine whether thetriangles are similar.

�DAC

F� � �69� � �

23�

�BE

CF� � �1

82� � �

23�

�DAB

E� � �1105� � �

23�

�ABC � �DEF by SSS Similarity.

15

129

D E

F

10

86

A B

C

Determine whether thetriangles are similar.

�34� � �

68�, so �MQR

N� � �

NRS

P�.

m�N � m�R, so �N � �R.�NMP � �RQS by SAS Similarity.

8

4

70�

Q

R S6

370�

M

N P

Determine whether each pair of triangles is similar. Justify your answer.

1. 2.

3. 4.

5. 6. 32

20

154025

24

3926

1624

18

8

65�9

465�

36

2018

24

Example 1 Example 2

Exercises

Less

on

7-3

05-42 Geo-07-873964 4/12/06 8:44 PM Page 21



Similar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

7-3C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

Use Similar Triangles Similar triangles can be used to find measurements.

�ABC � �DEF.Find x and y.

�DAC

F� � �BE

CF� �D

ABE� � �

BE

CF�

� �198� �1

y8� � �

198�

18x � 9(18�3�) 9y � 324x � 9�3� y � 36

18�3��x

18��3

B

CA

18 18 9y

x

E

FD

A person 6 feet tall castsa 1.5-foot-long shadow at the same timethat a flagpole casts a 7-foot-longshadow. How tall is the flagpole?

The sun’s rays form similar triangles.Using x for the height of the pole, �

6x� � �

17.5�,

so 1.5x � 42 and x � 28.The flagpole is 28 feet tall.

7 ft

6 ft?

1.5 ft

Each pair of triangles is similar. Find x and y.

1. 2.

3. 4.

5. 6.

7. The heights of two vertical posts are 2 meters and 0.45 meter. When the shorter postcasts a shadow that is 0.85 meter long, what is the length of the longer post’s shadow to the nearest hundredth?

y

x32

10

2230yx

9

8

7.2

16

yx

6038.6

23

3024

36��2yx

3636

20

13

26y

x � 235

13

10 20y

x

Example 1 Example 2

Exercises

05-42 Geo-07-873964 4/12/06 8:44 PM Page 22


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Skills PracticeSimilar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

7-3


1. 2.

3. 4.

ALGEBRA Identify the similar triangles, and find x and the measures of theindicated sides.

5. A�C� and E�D� 6. J�L� and L�M�

7. E�H� and E�F� 8. V�T� and S�T�

6

14

S

U

V

R T

x � 4

x � 612

9

6

9

D

E

FH

Gx � 5

16

4M

NL

J

K

x � 18

x � 3

1512

D

E CB

Ax � 1

x � 5

30�60�RQ

M

S

K

T

2170�

15

MJ

P

1470�10

U

S

T

12

128

9

9 6

C P

QR

A

B

2014

13 1221

9

S W X

Y

R

T

Less

on

7-3

05-42 Geo-07-873964 4/12/06 8:44 PM Page 23


PracticeSimilar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

7-3C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.


1. 2.

ALGEBRA Identify the similar triangles, and find x and the measures of theindicated sides.

3. L�M� and Q�P� 4. N�L� and M�L�

Use the given information to find each measure.

5. If T�S� || Q�R�, TS � 6, PS � x � 7, 6. If E�F� || H�I�, EF � 3, EG � x � 1,QR � 8, and SR � x � 1, HI � 4, and HG � x � 3,find PS and PR. find EG and HG.

INDIRECT MEASUREMENT For Exercises 7 and 8, use the following information.A lighthouse casts a 128-foot shadow. A nearby lamppost that measures 5 feet 3 inches castsan 8-foot shadow.

7. Write a proportion that can be used to determine the height of the lighthouse.

8. What is the height of the lighthouse?

F

GE

H

I

S RP

QT

8

N

J LK

Mx � 5

6x � 2

24

12

18N

P

QL

M

x � 3x � 1

18

16 12.516

14

11

M

L N

S R

T42�

42�

24

1812

16J

A K

Y S

W

05-42 Geo-07-873964 4/12/06 8:44 PM Page 24


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeSimilar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

7-3

Less

on

7-3

1. MINIATURES Marla likes her chair so much that she decides to make aminiature replica of it for her pethamster. Find the value of x.

2. MODELS Jim has a scale model of hissailboat. The figure shows drawings ofthe original sailboat and the model.Find x.

3. GEOMETRY Georgia draws a regularpentagon and starts connecting itsvertices to make a 5-pointed star. Afterdrawing three of thelines in the star, shebecomes curiousabout two trianglesthat appear in thefigure, �ABC and�BCE. They look similar to her. Provethat this is the case.

4. SHADOWS A radio tower casts ashadow 8 feet long at the same time that a vertical yardstick casts a shadowhalf an inch long. How tall is the radiotower?

MOUNTAIN PEAKS For Exercises 5 and6, use the following information.Gavin and Brianna want to know how far amountain peak is from their houses. Theymeasure the angles between the line of siteto the peak and to each other’s houses andcarefully make the drawing shown.

The actual distance between Gavin and Brianna’s house is 1�

12� miles.

5. What is the actual distance of themountain peak from Gavin’s house?Round your answer to the nearest tenth of a mile.

6. What is the actual distance of themountain peak from Brianna’s house?Round your answer to the nearest tenth of a mile.

Gavin

Brianna

Peak

2 in.

2.015 in.0.246 in.

90˚83˚

A

B

D

E

C

52˚

203 in.

10.15 in. 8 in.52˚

x in.

14”

3.5”

15”

x

05-42 Geo-07-873964 4/12/06 8:44 PM Page 25


Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

7-3

Moving ShadowsHave you ever watched your shadow as you walked along the street at night and observedhow its shape changes as you move? Supposea man who is 6 feet tall is standing below a lamppost that is 20 feet tall. The man iswalking away from the lamppost at a rate of 5 feet per second.

1. If the man is moving at a rate of 5 feet persecond, make a conjecture as to the ratethat his shadow is moving.

2. How far away from the lamppost is the man after 8 seconds?

3. How far is the end of his shadow from the bottom of the lamppost after 8 seconds? Use similar triangles to solve this problem.

4. After 3 more seconds, how far from the lamppost is the man? How far from thelamppost is his shadow?

5. How many feet did the man move in 3 seconds? How many feet did the shadowmove in 3 seconds?

6. The man is moving at a rate of 5 feet/second. What rate is his shadow moving?How does this rate compare to the conjecture you made in problem 1? Make aconjecture as to why the results are like this.

20 ft

6 ft

x ft

5 ft/sec

Copyright ©

Glencoe/M

cGraw

-Hill, a division of T

he McG

raw-H

ill Com

panies, Inc.

05-42 Geo-07-873964 4/12/06 8:45 PM Page 26


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Lesson Reading GuideParallel Lines and Proportional Parts

NAME ______________________________________________ DATE ____________ PERIOD _____

7-4


Use a geometric idea to explain why the distance between Chicago Avenue andOntario Street is shorter along Michigan Avenue than along Lake Shore Drive.

Read the Lesson

1. Provide the missing words to complete the statement of each theorem. Then state thename of the theorem.

a. If a line intersects two sides of a triangle and separates the sides into corresponding

segments of lengths, then the line is to the

third side.

b. A midsegment of a triangle is to one side of the triangle and its

length is the length of that side.

c. If a line is to one side of a triangle and intersects the other two sides

in distinct points, then it separates these sides into

of proportional length.

2. Refer to the figure at the right.

a. Name the three midsegments of �RST.

b. If RS � 8, RU � 3, and TW � 5, find the length of each of themidsegments.

c. What is the perimeter of �RST?

d. What is the perimeter of �UVW?

e. What are the perimeters of �RUV, �SVW, and �TUW?

f. How are the perimeters of each of the four small triangles related to the perimeter ofthe large triangle?

g. Would the relationship that you found in part f apply to any triangle in which themidpoints of the three sides are connected?


3. A good way to remember a new mathematical term is to relate it to other mathematicalvocabulary that you already know. What is an easy way to remember the definition ofmidsegment using other geometric terms?

R

U

V

W

T

S

Less

on

7-4

05-42 Geo-07-873964 4/12/06 8:45 PM Page 27


Study Guide and InterventionParallel Lines and Proportional Parts

NAME ______________________________________________ DATE ____________ PERIOD _____

7-4C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

Proportional Parts of Triangles In any triangle, a line parallel to one side of a triangle separates the other two sides proportionally. The converse is also true.

If X and Y are the midpoints of R�T� and S�T�, then X�Y� is amidsegment of the triangle. The Triangle Midsegment Theoremstates that a midsegment is parallel to the third side and is half its length.

If XY�� || RS��, then �RXTX� � �Y

SYT�.

If �RXTX� � �Y

SYT�, then XY�� || RS��.

If X�Y� is a midsegment, then XY�� || RS�� and XY � �12�RS.

Y ST

R

X

In �ABC, E�F� || C�B�. Find x.

Since E�F� || C�B�, �FA

BF� � �E

AEC�.

�xx

��

222

� � �168�

6x � 132 � 18x � 3696 � 12x8 � x

F

C

BA

18

x � 22 x � 2

6E

A triangle has verticesD(3, 6), E(�3, �2), and F(7, �2).Midsegment G�H� is parallel to E�F�. Find the length of G�H�.G�H� is a midsegment, so its length is one-half that of E�F�. Points E and F have thesame y-coordinate, so EF � 7 � (�3) � 10.The length of midsegment G�H� is 5.

Find x.

1. 2. 3.

4. 5. 6.

7. In Example 2, find the slope of E�F� and show that E�F� || G�H�.

30 10x � 10

x11x � 12

x33

30 10

24x

35

x9

20

x

185

5 x

7

Example 1 Example 2

Exercises

05-42 Geo-07-873964 4/12/06 8:45 PM Page 28


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.


Parallel Lines and Proportional Parts

NAME ______________________________________________ DATE ____________ PERIOD _____

7-4

Divide Segments Proportionally When three or more parallel lines cut two transversals,they separate the transversals into proportional parts. If the ratio of the parts is 1, then the parallellines separate the transversals into congruent parts.

If �1 || �2 || �3, If �4 || �5 || �6 and

then �ab� � �d

c�. �

uv� � 1, then �

wx� � 1.

Refer to lines �1, �2 ,and �3 above. If a � 3, b � 8, and c � 5, find d.

�1 || �2 || �3 so �38� � �d

5�. Then 3d � 40 and d � 13�

13�.

Find x and y.

1. 2.

3. 4.

5. 6.16 32

y � 3y

3 4

x � 4x

5

8 y � 2

y2x � 4

3x � 1 2y � 2

3y

2x � 6

x � 3

12

x � 12 12

3x5x

a

bd

u v

xw

ctn

m

s �1

�4 �5 �6

�2

�3

Example

Exercises

Less

on

7-4

05-42 Geo-07-873964 4/12/06 8:45 PM Page 29


Skills PracticeParallel Lines and Proportional Parts

NAME ______________________________________________ DATE ____________ PERIOD _____

7-4C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

1. If JK � 7, KH � 21, and JL � 6, 2. Find x and TV if RU � 8, US � 14,find LI. TV � x � 1 and VS � 17.5.

Determine whether B�C� || D�E�.

3. AD � 15, DB � 12, AE � 10, and EC � 8

4. BD � 9, BA � 27, and CE is one third of EA

5. AE � 30, AC � 45, and AD is twice DB

COORDINATE GEOMETRY For Exercises 6–8, use the following information.Triangle ABC has vertices A(�5, 2), B(1, 8), and C(4, 2). Point Dis the midpoint of A�B� and E is the midpoint of A�C�.

6. Identify the coordinates of D and E.

7. Show that B�C� is parallel to D�E�.

8. Show that DE � �12�BC.

9. Find x and y. 10. Find x and y.

3–2x � 2

x � 3

2y � 1

3y � 52x � 1 3y � 8

y � 5x � 7

x

y

O

A C

B

D

E

C

B

E

D

A

R

U V

T

S

HL

K J

I

05-42 Geo-07-873964 4/12/06 8:45 PM Page 30


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

PracticeParallel Lines and Proportional Parts

NAME ______________________________________________ DATE ____________ PERIOD _____

7-4

1. If AD � 24, DB � 27, and EB � 18, 2. Find x, QT, and TR if QT � x � 6,find CE. SR � 12, PS � 27, and TR � x � 4.

Determine whether J�K� || N�M�.

3. JN � 18, JL � 30, KM � 21, and ML � 35

4. KM � 24, KL � 44, and NL � �56�JN

COORDINATE GEOMETRY For Exercises 5 and 6, use the following information.Triangle EFG has vertices E(�4, �1), F(2, 5), and G(2, �1). Point Kis the midpoint of E�G� and H is the midpoint of F�G�.

5. Show that E�F� is parallel to K�H�.

6. Show that KH � �12�EF.

7. Find x and y. 8. Find x and y.

9. MAPS The distance from Wilmington to Ash Grove along Kendall is 820 feet and along Magnolia, 660 feet. If the distance between Beech and Ash Grove along Magnolia is 280 feet, what is the distance between the two streets alongKendall?

Ash Grove

Beech

Magnolia Kendall

Wilmington

4–3y � 2

3x � 4 x � 1

4y � 43x � 4

2–3y � 3

1–3y � 65–

4x � 3

x

y

O

E G

F

H

K

N LJ

KM

S

Q

TRP

D

E

C

BA

Less

on

7-4

05-42 Geo-07-873964 4/12/06 8:45 PM Page 31


Word Problem PracticeParallel Lines and Proportional Parts

NAME ______________________________________________ DATE ____________ PERIOD _____

7-4C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

1. CARPENTRY Jake isfixing an A-frame.He wants to add ahorizontal supportbeam halfway up and parallel to the ground. Howlong should thisbeam be?

2. STREETS In the diagram, Cay Streetand Bay Street are parallel. Find x.

3. JUNGLE GYMS Prassad is building atwo-story jungle gym according to theplans shown. Find x.

4. FIREMEN A cat is stuck in a treeand firemen try torescue it. Basedon the figure, if afireman climbs to the top of theladder, how faraway is the cat?

EQUAL PARTS For Exercises 5 and 6,use the following information.Nick has a stick that he would like to divide into 9 equal parts. He places it on a piece of grid paper as shown. The grid paper is ruled so that vertical andhorizontal lines are equally spaced.

5. Explain how he can use the grid paperto help him find where he needs to cutthe stick.

6. Suppose Nick wants to divide his stickinto 5 equal parts utilizing the gridpaper. What can he do?

Meeeeowww!

30 ft.

40 ft.46 ft.

x

8 ft. 8 ft.

10 ft.

24 ft

.

10 ft.x

Cay St.

1 km 1.4 km

0.8 km

Bay St.

Dale

St. Earl St.

(not drawn to scale)

x

8 feet

05-42 Geo-07-873964 4/12/06 8:45 PM Page 32


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.


7-4

Parallel Lines and Congruent PartsThere is a theorem stating that if three parallel lines cut off congruent segments on onetransversal, then they cut off congruent segments on any transversal. This can be shown forany number of parallel lines. The following drafting technique uses this fact to divide asegment into congruent parts.

A�B� is to be separated into five congruent parts. This can be done very accurately without using a ruler. All that is needed is a compass and a piece of notebook paper.

Step 1 Hold the corner of a piece of notebook paper at point A.

Step 2 From point A, draw a segment along the paper that is five spaces long. Mark where the lines of the notebook paper meet the segment. Label the fifth point, P.

Step 3 Draw P�B�. Through each of the other marks on A�P�, construct a line parallel to B�P�. The points where these lines intersect A�B� will divide A�B� into five congruent segments.

Use a compass and a piece of notebook paper to divide each segment into the given number of congruent parts.

1. six congruent parts

2. seven congruent parts A B

A B

A

P

B

A B

P

A B

A B

Less

on

7-4

05-42 Geo-07-873964 4/12/06 8:45 PM Page 33


Lesson Reading GuideParts of Similar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

7-5C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.


• How is similarity involved in the process of making a photographic print from anegative?

• Why do photographers place their cameras on tripods?

Read the Lesson

1. In the figure, �RST � �UVW. Complete each proportion involving the lengths of segments inthis figure by replacing the question mark. Thenidentify the definition or theorem from the listbelow that the completed proportion illustrates.

i. Definition of congruent polygons ii. Definition of similar polygons

iii. Proportional Perimeters Theorem iv. Angle Bisectors Theorem

v. Similar triangles have corresponding altitudes proportional to corresponding sides.

vi. Similar triangles have corresponding medians proportional to corresponding sides.

vii. Similar triangles have corresponding angle bisectors proportional to corresponding sides.

a. �RS � S?T � TR� � �U

RSV� b. �U

RWT� � �

S?X�

c. �RU

MN� � �V

?W� d. �U

RSV� � �

S?T�

e. �RPS

P� � �S

?T� f. �

U?N� � �

UR

WT�

g. �WTP

Q� � �R?T� h. �

UVW

W� � �Q

?V�


2. A good way to remember a large amount of information is to remember key words. Whatkey words will help you remember the features of similar triangles that are proportionalto the lengths of the corresponding sides?

W

Q N

YU

V

T

P M

XR

S

05-42 Geo-07-873964 4/12/06 8:45 PM Page 34


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Study Guide and InterventionParts of Similar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

7-5

Perimeters If two triangles are similar, their perimeters have the same proportion as the corresponding sides.

If �ABC � �RST, then

�AR

BS

��

BST

C��

RA

TC

� � �AR

BS� � �

BST

C� � �R

ACT�.

Use the diagram above with �ABC � �RST. If AB � 24 and RS � 15,find the ratio of their perimeters.Since �ABC � �RST, the ratio of the perimeters of �ABC and �RST is the same as theratio of corresponding sides.

Therefore � �2145�

� �85�

Each pair of triangles is similar. Find the perimeter of the indicated triangle.

1. �XYZ 2. �BDE

3. �ABC 4. �XYZ

5. �ABC 6. �RST

25

20

10

P T

SM

R

95

13

12

A D

E

C

B

5 6

8.7

13

10

X Y

Z T

R S18

20

25 15 17

8

NB

A C PM

36

9

11C

DE

A

B

44

24

20 22 10

TRX Z

YS

perimeter of �ABC��perimeter of �RST

A C

BS

R T

Example

Exercises

Less

on

7-5

05-42 Geo-07-873964 4/12/06 8:45 PM Page 35



Parts of Similar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

7-5C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

Special Segments of Similar Triangles When two triangles are similar,corresponding altitudes, angle bisectors, and medians are proportional to the correspondingsides. Also, in any triangle an angle bisector separates the opposite side into segments thathave the same ratio as the other two sides of the triangle.

In the figure,�ABC � �XYZ, with angle bisectors asshown. Find x.

Since �ABC � �XYZ, the measures of theangle bisectors are proportional to themeasures of a pair of corresponding sides.

�AX

BY� � �Y

BWD�

�2x4� � �

180�

10x � 24(8)10x � 192

x � 19.2

2410

DW

Y

ZXC

B

A

8x

S�U� bisects �RST. Find x.

Since S�U� is an angle bisector, �RTU

U� � �

RTS

S�.

�2x0� � �

1350�

30x � 20(15)30x � 300

x � 10

x 20

3015

UT

S

R

Find x for each pair of similar triangles.

1. 2.

3. 4.

5. 6. 2x � 2x � 1

281617

11

x � 7

x

10

10x

8

873

3

4x

69

12x

x

36

1820

Example 1 Example 2

Exercises

05-42 Geo-07-873964 4/12/06 8:45 PM Page 36


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Skills PracticeParts of Similar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

7-5

Find the perimeter of the given triangle.

1. �JKL, if �JKL � �RST, RS � 14, 2. �DEF, if �DEF � �ABC, AB � 27,ST � 12, TR � 10, and LJ � 14 BC � 16, CA � 25, and FD � 15

3. �PQR, if �PQR � �LMN, LM � 16, 4. �KLM, if �KLM � �FGH, FG � 30,MN � 14, NL � 27, and RP � 18 GH � 38, HF � 38, and KL � 24


5. Find FG if �RST � �EFG, S�H� is an 6. Find MN if �ABC � �MNP, A�D� is an altitude of �RST, F�J� is an altitude of altitude of �ABC, M�Q� is an altitude of�EFG, ST � 6, SH � 5, and FJ � 7. �MNP, AB � 24, AD � 14, and MQ � 10.5.

Find x.

7. �HKL � �XYZ 8.

LH

K

18

10

Y

15

x

ZX7

20

24

x

C

A

BD P NQ

M

JGE

F

HTR

S

GL

K

M

F

H

L MP Q

RN

A

B

C

D

E

F

R S

T

J K

L

Less

on

7-5

05-42 Geo-07-873964 4/12/06 8:45 PM Page 37


PracticeParts of Similar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

7-5C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

Find the perimeter of the given triangle.

1. �DEF, if �ABC � �DEF, AB � 36, 2. �STU, if �STU � �KLM, KL � 12,BC � 20, CA � 40, and DE � 35 LM � 31, MK � 32, and US � 28


3. Find PR if �JKL � �NPR, K�M� is an 4. Find ZY if �STU � �XYZ, U�A� is an altitude of �JKL, P�T� is an altitude of altitude of �STU, Z�B� is an altitude of �NPR, KL � 28, KM � 18, and �XYZ, UT � 8.5, UA � 6, and PT � 15.75. ZB � 11.4.

Find x.

5. 6.

PHOTOGRAPHY For Exercises 7 and 8, use the following information.Francine has a camera in which the distance from the lens to the film is 24 millimeters.

7. If Francine takes a full-length photograph of her friend from a distance of 3 meters andthe height of her friend is 140 centimeters, what will be the height of the image on thefilm? (Hint: Convert to the same unit of measure.)

8. Suppose the height of the image on the film of her friend is 15 millimeters. If Francinetook a full-length shot, what was the distance between the camera and her friend?

x28

20 30402x � 1 25x � 4

YX B

Z

TS A

U

MJ L

K

TN R

P

KS

LT

UMBE

CFD

A

05-42 Geo-07-873964 4/12/06 8:45 PM Page 38


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Word Problem PracticeParts of Similar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

7-5

Less

on

7-5

1. JOGGING Macy wants to jog aroundTriangle Park. On a scale map, the parkhas a perimeter of 11 inches. The scaleof the map is 1 inch : 100 yards. What isthe perimeter of the actual park?

2. TENTS Jana went camping and stayedin a tent shaped like a triangle. In aphoto of the tent, the base of the tent is6 inches and the altitude is 5 inches. Theactual base was 12 feet long. What wasthe height of the actual tent?

3. PLAYGROUND The playground atHank’s school has a large right trianglepainted in the ground. Hank starts at the right angle corner and walkstoward the opposite side along an anglebisector and stops when he gets to thehypotenuse.

How much farther from Hank is point Bversus point A?

4. FLAG POLES A flag pole attached tothe side of a building is supported with a network of strings as shown in thefigure.

The rigging is done so that AE � EF,AC � CD, and AB � BC. What is theratio of CF to BE?

COPIES For Exercises 5 and 6, use thefollowing information.Gordon made a photocopy of a page from his geometry book to enlarge one of thefigures. The actual figure that he copied isshown below.

The photocopy came out poorly. Gordoncould not read the numbers on thephotocopy, although the triangle itself was clear. Gordon measured the base of the enlarged triangle and found it to be 200 millimeters.

5. What is the length of the drawn altitudeof the enlarged triangle? Round youranswer to the nearest millimeter.

6. What is the length of the drawn medianof the enlarged triangle? Round youranswer to the nearest millimeter.

39 mm

Med

ian

Altit

ude

30 mm

29 mm

A BC

DF

E

A

B

45˚

30 ft

40 ft

50 ft

x

05-42 Geo-07-873964 4/12/06 8:45 PM Page 39

Another Proof of Pythagorean Theorem

1. For right triangle ABC with right angle C, and altitude C�D� as shown at the right, name three similar triangles.

2. List the three similar triangles as headings in the table below. Use the figure to complete thetable to list the corresponding parts of the threesimilar right triangles.

3. Use the corresponding parts of these similar triangles and their proportions to complete the statements in the proof and algebraically prove the Pythagorean Theorem.

Statements Reasons

1. Right triangle ABC with 1. Givenaltitute C�D�.

2. 2. Corresponding parts of similartriangles are in the same ratio

3. 3. Cross Products

4. 4. Addition Property of Equality

5. 5. Substitution

6. 6. Distribution Property

7. 7. Segment addition

8. a2 � b2 � c2 8. Substitution

A

a b

d e

c

B

C

D


Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

7-5C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

Short Leg

Long Leg

Hypotenuse

05-42 Geo-07-873964 4/12/06 8:45 PM Page 40


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Spreadsheet ActivityFractals

NAME ______________________________________________ DATE ____________ PERIOD _____

7-5

You can use a spreadsheet to create a Sierpinski triangle.

Use a spreadsheet to create a Sierpinski triangle.

Step 1 In cell A2, enter 1. In cell A3, enter an equals sign followed by A2�1 . This willreturn the number of iterations. Click on the bottom right corner of cell A2 anddrag it through cell A500 to get 500 iterations.

Step 2 In cell B1, enter 0.5. This indicates the midpoints of the segments.Step 3 In cell C1, enter 1 and in cell D1, enter 0.3.Step 4 In cell B2, enter an equals sign followed by 3*RAND(). Click on the bottom right

corner of cell B2 and drag in through cell B500 to get 500 iterations.Step 5 In cell C2, enter an equals sign followed by the recursive formula

IF(B2<1,(1�$B$1)*C1,IF(B22,(1�$B$1)*C1�$B$1,(1�$B$1)*C1�2*$B$1)). Thiswill return the x values of the points to be graphed. Click on the bottom right corner of cell C2 and drag through cell C500.

Step 6 In cell D2, enter an equals sign followed by the recursive formulaIF(B21,(1�$B$1)*D1,IF(B22,(1�$B$1)*D1�$B$1,(1�$B$1)*D1)). This willreturn the y values of the points to be graphed. Click on the bottom right corner ofcell D2 and drag throughcell D500.

Step 7 To graph the values incolumns C and D, first highlight all of the data in the two columns. Next,choose the chart wizardfrom the toolbar. Select XY(Scatter). Press Next, Next.Then select the Gridlinestab and uncheck the Major gridlines. Then press Next and Finish.This will return the Sierpinski triangle.

Analyze your drawing.1. What happens to your drawing if you have more iterations? Try 1000, 2000, and 5000.

2. Change the 0.5 to 2\3 in cell B1. (Hint: You may need to enter 0.666666 for 2\3.) Howdoes this change the picture?

3. Change 0.3 to 0.6 in cell D1. How does this change the drawing? 4. Enter the following into a new spreadsheet and describe what you see.

Step 1: In cell A2, enter the formula � A1.Step 2: In cell B2, enter the formula � A1�B1.Step 3: Click on the bottom right corner of cell B2 and drag through cell L2.Step 4: First, click on the 2 next to cell A2. Then, click on the bottom left corner of 2

and drag down through cell 12.Step 5: In cell A1, enter a 1 and press ENTER.

Sheet 1 Sheet 2 Sheet 3

Less

on

7-5

Example

Exercises

05-42 Geo-07-873964 4/12/06 8:45 PM Page 41

05-42 Geo-07-873964 4/12/06 8:45 PM Page 42


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Student Recording SheetUse this recording sheet with pages 428–429 of the Student Edition.

NAME ______________________________________________ DATE ____________ PERIOD _____

7

1.

2.

3. Record your answer and fill in thebubbles in the grid below. Be sure to use the correct place value.

4.

5.

6. Record your answer and fill in thebubbles in the grid below. Be sure to use the correct place value.

7.

8.

9.

10.

11.

12.

Record your answers for Question 13on the back of this paper.

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

.

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

F G H J

A B C D

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

.

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

F G H J

A B C D

Read each question. Then fill in the correct answer.

Ass

essm

ent

Pre-AP

SCORE _____


Rubric for Scoring Pre-AP(Use to score the Pre-AP question on page 429 of the Student Edition.)

NAME ______________________________________________ DATE ____________ PERIOD _____

7C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

General Scoring Guidelines

• If a student gives only a correct numerical answer to a problem but does not showhow he or she arrived at the answer, the student will be awarded only 1 credit.All extended-response questions require the student to show work.

• A fully correct answer for a multiple-part question requires correct responses forall parts of the question. For example, if a question has three parts, the correctresponse to one or two parts of the question that required work to be shown is notconsidered a fully correct response.

• Students who use trial and error to solve a problem must show their method.Merely showing that the answer checks or is correct is not considered a completeresponse for full credit.

Exercise 13 Rubric

Score Specific Criteria

4 An understanding that �ADE � �ADE is shown by using the TriangleProportionality Theorem, which states that if a line is parallel to one side of a triangle and intersects the other two sides in two distinct points,then it separates these sides into segments of proportional length, so

�AA

EC� � �

AA

DB�. Since the corresponding sides are proportional and the

included angle, �A, is the same, by the SAS Similarity Theorem we knowthat the triangles are similar. The correct proportion is set up in part b todetermine whether the missing value is 800 ft or 2000 ft.

3 A generally correct solution, but may contain minor flaws in reasoning or computation.

2 A partially correct interpretation and/or solution to the problem.

1 A correct solution with no evidence or explanation.

0 An incorrect solution indicating no mathematical understanding of theconcept or task, or no solution is given.

SCORE _____


Chapter 7 Quiz 1(Lessons 7–1 and 7–2)

NAME ______________________________________________ DATE ____________ PERIOD _____

7

Ass

essm

ent

SCORE _____Chapter 7 Quiz 2(Lesson 7–3)

NAME ______________________________________________ DATE ____________ PERIOD _____

7

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

1.

2.

3.

4.

5.

1. GARDENS The model of a circular garden is 8 inches indiameter. The actual garden will be 20 feet in diameter. Findthe ratio of the diameter of the model to the diameter of theactual garden.

2. PHOTOS A 4-inch by 6-inch photograph, set vertically, isenlarged to make a poster 22 inches wide. How tall is the poster?

3. Are any of the three trianglessimilar? If so, write theappropriate similaritystatement.

4. If �ABC � �DEC, find x and the scale factor of �ABC to �DEC.

5. MULTIPLE CHOICE In a rectangle, the ratio of the length tothe width is 5:2, and its perimeter is 126 centimeters. Find thewidth of the rectangle.A. 9 cm B. 18 cm C. 45 cm D. 50.4 cm

D

E

CB

A

20

253x � 2

2x

BP X Y

Z

Q

R

A

C

5

4 8 8 8

10

4

1.

2.

3.

4.

5.

For Questions 1 and 2, determine whether each pair oftriangles is similar. Justify your answer.

1. 2.

3. Identify the similar triangles in the figure,then find x.

4. SHADOWS A person who is 5 feet tall casts a shadow that is4 feet long. At the same time, a flagpole casts a shadow that is18 feet long. Find the height of the flagpole.

5. Find x in the figure.

46

9 x

8

A

B D

EF

C 4

6x

20

15

98

10 1241�

52�41�

87�

SCORE _____


Chapter 7 Quiz 3(Lesson 7–4)

NAME ______________________________________________ DATE ____________ PERIOD _____

7C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

SCORE _____Chapter 7 Quiz 4(Lesson 7–5)

NAME ______________________________________________ DATE ____________ PERIOD _____

7

1.

2.

3.

4.

5.

1. Determine whether M�N� || K�L�.Justify your answer.

2. Find x so that L�M� || A�B�.

3. In �ABC, D�E� is parallel to A�C� and DE � 10. Find the length of A�C� if D�E� is the midsegment of �ABC .

4. Find DE.

5. A triangle QRS has vertices Q(�2, 3), R(�2, �3), and S(8, 1).TU is the midsegment of QRS and is parallel to QR. What arethe coordinates of T and U?

20

12

15 DE

B

A

C

6 8

4A B

C

L Mx

J

M

N11

2

3

9

L

K

1.

2.

3.

4.

5.

1. If �PQR � � XYZ, find the perimeter of �XYZ.

For Questions 2–4, refer to the trianglesABC and DEF. �ABC � �DEF. Theperimeter of �ABC is 48 cm and theperimeter of �DEF is 32 cm.

2. Find the length of D�E� to the nearesttenth.

3. What is the relationship between the corresponding altitudes B�X� and E�Y�?

4. Find the length of E�Y� to the nearesttenth.

5. In �RST, TU�� bisects �T. If U is a point on R�S�, RU � 6,RT � 9, and ST � 12, find RS.

D F

E

Y

A C

B

128

X

16

128

P R

Q

5

X Z

Y

SCORE _____


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 7 Mid-Chapter Test(Lessons 7–1 through 7–3)

NAME ______________________________________________ DATE ____________ PERIOD _____

7

Ass

essm

ent

1. Polygon ABCD is similar to polygon PQRS. Which proportion must be true?

A. �AA

DC� � �

PP

QS� B. �C

BDC� � �

QR

RS� C. �B

ADB� � �Q

PQR� D. �

CA

DB� � �

PR

QS�

2. This fall, 126 students participated in the soccer program, while 54 playedvolleyball. What was the ratio of soccer players to volleyball players?

F. �34� G. �

37� H. �

43� J. �

73�

3. The ratio of the measures of the angles of a triangle is 2:3:10. What is theleast angle measure?A. 12 B. 15 C. 24 D. 36

4. Find x.F. 2 H. 6G. 4.8 J. 6.4

5. Rectangle ABCD � rectangle EFGH, the perimeter of ABCD is 54 centimeters,and the perimeter of EFGH is 36 centimeters. What is the scale factor ofABCD to EFGH?

A. �23� B. �

32� C. �

35� D. �

53�

10 8

x

D

E

AC B18

6.

7.

8.

9.

10.

1.

2.

3.

4.

5.

Part II

For Questions 6 and 7, determine whether each pair oftriangles is similar. Justify your answer.

6. 7.

8. If �ABE � �BCD, find DE and the scale factor of �ABE to �BCD.

9. Quadrilateral ABCD � quadrilateral RSUV, m�ABC � 120,and the scale factor of ABCD to RSUV is �

85�. Find m�RSU.

10. MODELS Sasha made a model of a clipper ship. Her modelhas a length of 18 inches, and the original ship has a length of160 feet and a width of 32 feet. Find the width of the modelship.

24 32

9

A

B ED

C

45251810 85�85�6

415

10

Part I Write the letter for the correct answer in the blank at the right of each question.

SCORE _____


Chapter 7 Vocabulary Test

NAME ______________________________________________ DATE ____________ PERIOD _____

7C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

Choose the correct term to complete each sentence.

1. If there are 15 girls and 9 boys in an art class, the (ratio orscale factor) of girls to boys in the class is 5:3.

2. If �ABC � �DEF, AB �10, and DE � 2.5, then the (scalefactor or proportion) of �ABC to �DEF is 4:1.

Choose from the terms above to complete the sentence.

3. In �LMN, P lies on L�M� and Q on L�N�. If PQ � �12�MN, P�Q� is

called a(n) .

4. The product of the in the equation �3x� � �

2340� is 90.

5. The product of the in the equation �3x� � �

2340� is 24x.

State whether each sentence is true or false. If false,replace the underlined word or number to make a truesentence.

6. If quadrilaterals ABCD and WXYZ have corresponding anglescongruent and corresponding sides proportional, they arecalled .

7. The equation �3x� � �

2340� is called a(n) .

8. In a proportion, the cross products of the equals thecross product of the means.

Describe each phrase in your own words.

9. equality of cross products

10. midsegment

extremes

scale factor

cross products

?

?

?

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

cross productsextremesmeans

midsegmentproportionratio

scale factorsimilar polygons

SCORE _____


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 7 Test, Form 1NAME ______________________________________________ DATE ____________ PERIOD _____

7

Ass

essm

entWrite the letter for the correct answer in the blank at the right of each question.

1. There are 15 plums and 9 apples in a fruit bowl. What is the ratio of apples toplums?A. 3:5 B. 3:8 C. 5:3 D. 8:3

2. The scale drawing of a porch is 8 inches wide by 12 inches long. If the actualporch is 12 feet wide, what is the length of the porch?F. 8 ft G. 10 ft H. 16 ft J. 18 ft

3. Solve �56� � �

4x�.

A. 4.6 B. 4.8 C. 5 D. 7

4. A quality control technician checked a sample of 30 bulbs. Two of the bulbswere defective. If the sample was representative, find the number of bulbsexpected to be defective in a case of 450.F. 24 G. 30 H. 36 J. 45

5. Find the triangle similar to �ABC at the right.A. C.

B. D.

6. Find x if �ABC � �JKL.F. 10 H. 25G. 14 J. 29

7. Quadrilateral ABCD � quadrilateral PQRS. If AB � 10, BC � 6, PS � 12,and QR � 4, find the scale factor of ABCD to PQRS.

A. �12� B. �

32� C. �

53� D. �

56�

8. Quadrilateral ABCD � quadrilateral EFGH.Find x.F. 15 H. 25G. 20 J. 30

9. Which theorem or postulate can be used to prove that these two triangles are similar?A. AA B. SAS C. SSA D. SSS

10. Find MN.

F. 5�13� G. 6 �

34� H. 7 J. 12

35�8

96

35�

Q

PM

L

N

6

84

27�

63�

B

C

D

A

F

E

H

G 60� 120�80�

100�4x �

A C

B J L

K186 9

x � 2

4

35

15

36

39

2210

24

5

12

35

12

13

CB

A

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.


Chapter 7 Test, Form 1 (continued)

NAME ______________________________________________ DATE ____________ PERIOD _____

7C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

11.

12.

13.

14.

15.

16.

17.

18.

19.

11. A 5-foot tall student cast a 4-foot shadow. If the tree next to her cast a 44-footshadow, what is the height of the tree?

A. 35�15� ft B. 45 ft C. 51�

12� ft D. 55 ft

12. In �ABC, D�E� || A�C�. If AD � 12, BD � 3, and CE � 10,find BE.F. 1 H. 2

G. 1�12� J. 2�

12�

13. In �ABC A�C� || M�N�. What is x?A. 8 C. 25B. 10 D. 29

14. Find x.F. 14 H. 16G. 15 J. 18

15. �FGH � �PQR, FG � 6, PQ � 10, and the perimeter of �PQR is 35. What isthe perimeter of �FGH?A. 21 B. 27 C. 31 D. 58�

13�

16. �LMN � �XYZ with altitudes K�L�and W�X�. Find KL.F. 6 H. 9G. 7 J. 19

17. Find x.A. 5 C. 6�

12�

B. 6 D. 7�12�

18. Find x.F. 16 H. 20G. 18 J. 21

19. Nathan is building a model of his father’s sailboat with a scale factor of �312�.

The actual sail is in the shape of a right triangle with a base of 8 meters anda hypotenuse of 13 meters. What will be the approximate perimeter of the sailon the model boat?A. 32 cm B. 48.81 cm C. 65.62 cm D. 97.65 cm

Bonus In �ABC, AB � 10, BC � 16, D�E� ⊥ A�C�,and DE � 6. Find CD. 10

6B C

D

E

A

16

15

1824

x

1610

129x

28 123

K

L X

M YWZN

1610

24x

C B

A

N

M12

18

163x

C B

A

E

D12

10

3

B:

SCORE _____


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 7 Test, Form 2ANAME ______________________________________________ DATE ____________ PERIOD _____

7

Ass

essm


1. Of the 240 students eating lunch, 96 purchased their lunch and the restbrought a bag lunch. What is the ratio of students purchasing lunch tostudents bringing a bag lunch?A. 2:3 B. 2:5 C. 3:2 D. 5:2

2. In a rectangle, the ratio of the width to the length is 4:5. If the rectangle is 40 centimeters long, find its width.F. 32 cm G. 36 cm H. 44 cm J. 50 cm

3. A postage stamp 25 millimeters wide and 40 millimeter tall is enlarged tomake a poster. The poster is 4 feet wide. Find the height of the poster.A. 2.5 ft B. 5.25 ft C. 5.8 ft D. 6.4 ft

4. Find the polygon that is similar to ABCD.F. H.

G. J.

5. If �PQR � �STU, find x.A. 4.4 C. 24.6B. 7 D. 35

6. If ABCD � EFGH, find x.F. 18.75 H. 22.75G. 20 J. 28

7. �ABC � �LMN, AB � 18, BC � 12, LN � 9, and LM � 6. What is the scalefactor of �ABC to �LMN?

A. �92� B. �

32� C. �

31� D. �

21�

8. Name the theorem or postulate that can be used to prove that these triangles are similar.F. AA Similarity H. SAS SimilarityG. SSS Similarity J. SSA Similarity

For Questions 9 and 10, refer to the figure at the right.9. Identify the true statement.

A. �PQR � �RST C. �PQR � �TSRB. �PQR � �STR D. �PQR � �TRS

10. Find x.

F. 2�12� G. 3 H. 3�

12� J. 4

15

18

4x2

21–2

3

T

R

P

Q

S

14

43

7

16

30

10

x � 4

A

BC

DE H

GF

22�123�

5x�12 8

4.5

R U

S

TQ

P

88

2–3

2

2 618

6

4

12

A D

B C

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.


Chapter 7 Test, Form 2A (continued)

NAME ______________________________________________ DATE ____________ PERIOD _____

7C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

11.

12.

13.

14.

15.

16.

17.

18.

11. A 24-foot flagpole cast a 20-foot shadow. The building next to it cast an 85-footshadow. Find the height of the building.

A. 70�56� ft B. 89 ft C. 96�

16� ft D. 102 ft

12. Find QT.F. 15 H. 19G. 17 J. 21

13. Find x so that S�T� || P�R�.A. 4 C. 6

B. 4�12� D. 6�

12�

14. Find y.

F. �43� H. �

73�

G. 2 J. 3

15. If �KLM � �XYZ, find the perimeter of �XYZ.A. 40 C. 45B. 42 D. 48

16. �ABC � �JKL with altitudes B�X� and K�Y�.Find BX.F. 19.2 H. 24.6G. 21 J. 28

17. Find x.A. 4 C. 6B. 5 D. 8

18. Find y.

F. 2�14� H. 3�

12�

G. 2�34� J. 4�

12�

Bonus Find x.12

4 x

6

8

y

DA C

B

6S

Q

P R

12 8

x � 2 x

32

X CA

B10 6

Y LJ

K

9

X Z

Y4

K M

L7

9

69

2y

1–3y � 2

25

5

34x � 3 QR

P

S

T

24

40

35 RQ

PS

T

B:

SCORE _____


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 7 Test, Form 2BNAME ______________________________________________ DATE ____________ PERIOD _____

7

Ass

essm


1. Given the choice between doing an oral and a written report, 18 of the 28 students chose to do an oral report. Find the ratio of written to oral reports.A. 5:9 B. 9:5 C. 9:14 D. 14:9

2. A model of a lighthouse has diameter 8 inches and height 18 inches. If theactual diameter of the lighthouse is 20 feet, find its actual height.F. 30 ft G. 35 ft H. 45 ft J. 50 ft

3. The three sides of a triangle are in the ratio 2:4:5. If the shortest side of thetriangle is 4 meters long, find the perimeter.A. 17 m B. 22 m C. 32 m D. 40 m

4. Find the polygon that may be similar to ABCD.F. H.

G. J.

5. If �ABC � �DEF, find m�C.A. 54 C. 67B. 59 D. 69

6. Quadrilateral JKLM � quadrilateral WXYZ, JK � 15, LM � 10, XY � 6, andWX � 9. Find KL.F. 8 G. 10 H. 11 J. 12

7. �LMN � �RST, LN � 21, MN � 28, and the scale factor of �RST to �LMNis �

43�. Find ST.

A. 15�34� B. 21 C. 28 D. 37�

13�

8. Name the theorem or postulate that can be used to prove that these triangles are similar.F. AA Similarity H. SSA SimilarityG. SAS Similarity J. SSS Similarity

For Questions 9 and 10, refer to the figure at the right.9. Identify the similar triangles.

A. �LMN � �MPQ C. �LMN � �QPMB. �LMN � �QMP D. �LMN � �PQM

10. Find LM.F. 16 G. 17 H. 18 J. 20

1510 12

L

N

MP

Q

20

8

11.228

54�67�67�

DECA

FB

30

24

8

17

14

6

22

18

6

12

15

5

12

15

54

A B

D C

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.


Chapter 7 Test, Form 2B (continued)

NAME ______________________________________________ DATE ____________ PERIOD _____

7C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

11.

12.

13.

14.

15.

16.

17.

18.

11. A 6-foot tall fence post cast a 2�12�-foot shadow. A nearby clock tower cast a

35-foot shadow. What is the height of the tower?A. 37�

12� ft B. 71 ft C. 78 ft D. 84 ft

12. Find CE.F. 25 H. 27G. 26 J. 28

13. Find FH so that G�H� || D�E�.A. 4 C. 6B. 5 D. 7

14. Find x.F. 4 H. 9G. 6 J. 12

15. If �ABC � �PQR, find the perimeter of �PQR.

A. 12 C. 14�12�

B. 13�12� D. 16

16. �ABC � �XYZ with altitudes A�P�and X�Q�. Find AP.

F. 11�14� H. 15�

14�

G. 14 J. 20

17. Find x.A. 7 C. 9B. 8 D. 10

18. Find y.

F. 3�34� H. 6

G. 4 J. 7�12�

Bonus Find CE.6

5

4

39

A

B

C

D

E

6

21–4

16

y

R T

SU

40

16

x � 2

3x

125

Q

X

Y Z27

P

A

B C

6 Q

R

P8

7 3

B

C

A

58

2x

x � 3

9

10

15D

G

FE H

8

20

EB C

DA

35

B:

SCORE _____


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 7 Test, Form 2CNAME ______________________________________________ DATE ____________ PERIOD _____

7

Ass

essm

ent1. Of the 300 television sets sold at an electronics store last

month, 90 were flat-screen TVs. What is the ratio of flat-screenTVs to other TVs sold last month?

2. Determine whether �ABC � �DEF. Justify your answer.

3. When a 5-foot vertical pole casts a 3-foot, 4-inch shadow, anoak tree casts a 20-foot shadow. Find the height of the tree.

4. Quadrilateral ABCD � quadrilateral WXYZ, AB � 15, BC � 27,BC � 27, and the scale factor of WXYZ to ABCD is �

23�. Find XY.

5. The blueprint for a swimming pool is 8 inches by 2�12� inches.

The actual pool is 136 feet long. Find the width of the pool.

6. Find CD.

7. If quadrilateral ABCD � quadrilateral PQRS, find BC.

8. Determine whether �ABC � �DEF. Justify your answer.

9. �ABC � �XYZ, AB � 12, AC � 16, BC� 20, and XZ � 24.Find the perimeter of �XYZ.

For Questions 10 and 11, use the figure.

10. Identify the similar triangles.

11. Find x.

15 2x � 4

x6

P

Q

R S

T

9

8

6

42

5

B

EF

DC

A

28

10 6.5R

S P

Q B

A

C

D

1.8

2.46C EG

FD

22.5

15 1510

A

B

C DE

F

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.


Chapter 7 Test, Form 2C (continued)

NAME ______________________________________________ DATE ____________ PERIOD _____

7C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

12. If �ABC � �PQR and B�M� and Q�N� are medians, find BM.

13. The ratio of the measures of the three sides of a triangle is 3:4:6.If the perimeter is 91, find the measure of the longest side.

14. If �RST � �UVW, find m�W.

15. In �ABC, A�X� bisects �BAC. Find x.

16. Find y so that M�N� || B�C�.

17. �ABC � �LMN, and A�D� and L�P� are altitudes. Find AD.

18. Find x.

Bonus Find EG.18

10

12

B

F

D EG

C

A

28

818

2x � 2

13.5

3620

8D

A

C B M P

L

N

18

8y4

y

B

CAN

M

4x � 5

2x

8

6

A C

X

B

85�

48�R T

S

U W

V

11

4.43.8

A C P R

Q

B

M N

12.

13.

14.

15.

16.

17.

18.

B:

SCORE _____


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 7 Test, Form 2DNAME ______________________________________________ DATE ____________ PERIOD _____

7

Ass

essm

ent1. Of the 112 students in the marching band, 35 were in the

drum section. What is the ratio of drummers to othermusicians in the band?

2. Determine whether quadrilateral ABCD � quadrilateralEFGH. Justify your answer.

3. When a 9-foot tall garden shed cast a 5-foot, 3-inch shadow, ahouse cast a 28-foot shadow. Find the height of the house.

4. �ABC � �FGH, AB � 24, AC � 16, GH � 9, and FH � 12.Find the scale factor of �ABC to �FGH.

5. The model of a suspension bridge is 18 inches long and 2 inchestall. If the length of the actual bridge is 1650 feet, find its height.

6. Find GP.

7. If �JKL � �PQR, find x.

8. Determine whether �ABC � �PQR. Justify your answer.

9. �ABC � �PQR, AB � 18, BC � 20, AC � 22, and QR � 25.Find the perimeter of �PQR.

For Questions 10 and 11, use the figure.

10. Identify the similar triangles.

11. Find MN.20

x

6

Y Z

X

M

N

16

20

22.5

3012

158

P

BC

A

Q

R

35

14

6

x

J L

PQ

R

K

2.73.3

4.5

F H

Q

G

P

A

9

7

14 17

9 8.5

13.512

B

C

D H G

FE

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.


Chapter 7 Test, Form 2D (continued)

NAME ______________________________________________ DATE ____________ PERIOD _____

7C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

12. If �FGH � �LMN and A�F� and B�L� are medians, find BL.

13. The ratio of the measures of the three angles of a triangle is3:4:8. Find the measure of the largest angle.

14. If quadrilateral DEFG � quadrilateral WXYZ, find m�Y.

15. In �PQR, Q�S� bisects �PQR. Find x.

16. Find x so that P�Q� || F�H�.

17. If �FGH � �JKL, find GX.

18. Find y.

Bonus Find FG.

2.8 3.2 4.2

8 7

A

B F

GEC

D

42 2y

12 16

X Y

K

F H JL

27 12 21–2

G

63

3x2x � 1

F H

Q

G

P

P Q

R

S3x � 1

32

40

2x � 3

E F Z W

XY

GD

68� 85�

82�125�

16.8 4.8

7.7

F H L

MB

N

G

A

12.

13.

14.

15.

16.

17.

18.

B:

SCORE _____


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 7 Test, Form 3NAME ______________________________________________ DATE ____________ PERIOD _____

7

Ass

essm

ent1. In an orchard of apple and peach trees, �

37� of the trees are

peaches. What is the ratio of apple trees to peach trees?

2. Determine whether trapezoid ABCD � trapezoid PQRS.Justify your answer.

3. In �ABC, m�A � 51, AB � 14, and AC � 20. In �DEF,m�D � 51, DE � 16.8, and DF � 24. Determine whether�ABC � �DEF. Justify your answer.

4. A painting that is 48 inches by 12 inches is reduced to fit onan area that is 30 centimeters by 10 centimeters. Find themaximum dimensions of the reduced painting.

5. Find x.

6. If �ABC � �XYZ, find y.

7. The ratio of the measures of the sides of a triangle is 2:5:6. Ifthe length of the longest side is 48 inches, find the perimeter.

8. Find m�I.

9. �ABC � �DEF, AB � 8, BC � 13, AC � 15, and DF � 20.Find the perimeter of �DEF.

10. �ABC � �JKL, AB � 12, BC � 18.4, KL � 6.9, and JL � 5.6.Find the scale factor of �ABC to �JKL.

11. Find y.y � 8

4y � 7

F

G

HI

J45�

53�

17.5A C

B

2y

14X Z

Yy � 3

6

4.8

6.5K L

J

N

M

2x

9.6

15.6

12.47.8

9

15

6

23.4D

R S

PQ

C

A

B

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.


Chapter 7 Test, Form 3 (continued)

NAME ______________________________________________ DATE ____________ PERIOD _____

7C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

12. Find SR.

For Questions 13 and 14, �FGH � �JKL.

13. Find x.

14. Find the ratio of the perimeter of �FGH to the perimeter of �JKL.

15. Find AD so that D�E� || A�B�.

16. Find the fourth iterate of the expression 3x � 1, where xinitially equals 0.8.

17. When a 15-foot tall climbing wall cast a 20-foot shadow, abuilding cast a 32-foot shadow. Find the height of the building.

18. If �ABC � �EFG and B�D� and F�H� are medians, find BD.

Bonus The ratio of the lengths of the sides of �ABC is 5:2.5:4. The scale factor of �ABC to �DECis 5:2, and the scale factor of�DEC to �FEG is 1:4. B�C� is the shortest side and A�B� is thelongest side of �ABC. Find FG.

10

A

B C

D E

G

F

HE G

F2x � 5

751–4

x � 5

DA C

B

A B

ED

C

2x � 4 3x

8x5x

12x

F H

G7.5

4.5

J L

K

30 12Q

RPS

40

12.

13.

14.

15.

16.

17.

18.

B:

SCORE _____


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 7 Extended-Response TestNAME ______________________________________________ DATE ____________ PERIOD _____

7

Ass

essm

entDemonstrate your knowledge by giving a clear, concise solution to

each problem. Be sure to include all relevant drawings and justifyyour answers. You may show your solution in more than one way orinvestigate beyond the requirements of the problem.

1. Write a possible proportion if the extremes are 3 and 10.

2. �ABC and �WXY are isosceles triangles.

a. Write a possible ratio for the sides of �ABC if its perimeter is 42 inches.

b. Name possible measures for the sides of �ABC using your answer toPart a.

c. If �WXY has a perimeter of 28 and �ABC has sides with the measuresyou gave in Part b, what must be the measure of the sides of �WXY sothat �WXY � �ABC?

3. Write as many triangle similarity statements as possible for the figurebelow. How do you know that these triangles are similar?

4. Sketch two triangles that are not similar, but have one pair of correspondingangles congruent and two pairs of corresponding sides proportional. Labelthe corresponding angles and the proportional sides.

5.

a. Draw �XYZ inside �PQR with half the perimeter of �PQR. Explainyour process and why it works.

b. Draw the figure that results when your process in Part a is iterated 3 times.

c. Explain why your figure in Part b is a fractal.

d. The perimeter of �PQR is �12�x. If x equals 96, what is the perimeter of

the smallest triangle in your figure in Part b?

P R

Q

A B C D

I E

F

G

H

SCORE _____


Standardized Test Practice(Chapters 1–7)

NAME ______________________________________________ DATE ____________ PERIOD _____

7C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

1. Find the length of Y�Z�. (Lesson 1-2)

A 1.9 in. C 7.2 in.B 5.3 in. D 12.5 in.

2. Given: 3b � 4 � 16 Conjecture: b � 0Which of the following would be a counterexample? (Lesson 2-1)

F b � �1 G b � 0 H b � 3.5 J b � 4

3. Find the plane that is parallel to plane PTU. (Lesson 3-1)

A plane QRU C plane PQSB plane QRS D plane SPU

4. Find m�1. (Lesson 3-2)

F 5 H 41G 12 J 44

5. Which statement must be true in order to prove �ABC � �DCB by SAS? (Lesson 4-4)

A C�B� bisects �ABD.B �BCA � �CBDC �BDC � �CABD A�B� � B�C�

6. In an indirect proof, you assume that the conclusion is false andthen find a(n) . (Lesson 5-3)

F assumption H truth valueG contradiction J conditional statement

7. Demont and Tony are competing to see whose house is the tallest.Early in the afternoon, Tony, who is 4 feet tall, measured his shadowto be 9.6 inches and the shadow of his house to be 62.4 inches. Laterin the day, Demont, who is 5 feet tall, measured his shadow to be15.6 inches and the shadow of his house to be 62.4 inches. Who livesin the taller house? (Lesson 7-3)

A DemontB Both houses are the same height.C TonyD There is not enough information.

?

D

A C

B

(3x � 5)�

(125 � 7x)�

1

R

P

Q

STU

X Z5.5 in.

3.6 in. Y

Part 1: Multiple Choice

Instructions: Fill in the appropriate circle for the best answer.

1.

2.

3.

4.

5.

6.

7. 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


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

Standardized Test Practice (continued)

NAME ______________________________________________ DATE ____________ PERIOD _____

7

Ass

essm

ent8. Find the coordinates of the midpoint of AB for A(�24, 15) and

B(13, �31). (Lesson 1-3)

F (�18.5, �23) G (�11, �16) H (�5.5, �8) J (10.5, 23)

For Questions 9 and 10, use the figure at the right.

9. The perimeter of rectangle DEFG is 176, EF � h, and DE � 7h. What is h? (Lesson 1-6)

A 11 C 22B 15 D 77

10. What is the area of the rectangle DEFG? (Lesson 1-6)

F 88 units2 G 225 units2 H 513 units2 J 847 units2

11. What is the slope-intercept form for the line y � 7 � 4(x�10)?(Lesson 3-4)

A y � 4x � 47 B 4x � y � 47 C 4x � y � 17 D 4�xy� � 17

12. Which of the following is the equation of a line parallel to the linepassing through (4, �3) and (8, 5)? (Lesson 3-3)

F y � x � 2 G 2y � 9x � 4 H 2y � 2x � 4 J y � 2x � 9

D E

G F

8.

9.

10.

11.

12. F G H J

A B C D

F G H J

A B C D

F G H J

13. Find m�2. (Lesson 3-2)

14. �LMN is equilateral, LM is one more than threetimes a number, MN is nine less than five times thenumber, and NL is eleven more than the number.Find LM. (Lesson 4-1)

52�

12 34

Part 2: Griddable

Instructions: Enter your answer by writing each digit of theanswer in a column box and then shading in the appropriate circlethat corresponds to that entry.

13.

14.

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

.

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

.

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0


Standardized Test Practice (continued)

NAME ______________________________________________ DATE ____________ PERIOD _____

7C

opyright ©G

lencoe/McG

raw-H


cGraw

-Hill C

ompanies, Inc.

Part 3: Short Response

Instructions: Write your answers in the spaces provided.

15. Solve ��4106

� � �4x �

510

�. (Lesson 7-1)

16. X�A� is an altitude of �XYB. Find y.(Lesson 5-1)

17. Two sides of a triangle measure 21 inches and 32 inches, andthe third side measures x inches. Find the range for x. (Lesson 5-4)

18. If �ABC � �HIJ, find the perimeter of �HIJ. (Lesson 7-5)

19. Given T(3, �1), U(1, �7), V(8, �5), W(2, 6), X(�4, 8), and Y(�2, 1), determine whether �TUV � �WXY. Explain.(Lesson 4-3)

20. Given the points S(�5, 7), T(1, 9), P(12, �1), and R(3, 26):

a. Find the lengths of ST and PR to the nearest hundredth.(Lesson 3-6)

b. Determine the slope of ST and of PR. (Lesson 3-3)

c. Are ST and PR parallel, perpendicular, or neither? (Lesson 3-3)

32 cm

80 cm

60 cm

A B

C 12 cmH I

J

(2y � 81)� BA

X

Y

15.

16.

17.

18.

19.

20a.

20b.

20c.

Chapter 7 A1 Glencoe Geometry

Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

An

swer

s

Cha

pter

75

Gle

ncoe

Geo

met

ry

Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Less

on R

eadi

ng G

uide

Pro

po

rtio

ns

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-1

Get

Rea

dy

for

the

Less

on

Rea

d t

he

intr

odu

ctio

n t

o L

esso

n 7

-1 i

n y

our

text

boo

k.

Est

imat

e th

e ra

tio

of l

engt

h t

o w

idth

for

th

e ba

ckgr

oun

d re

ctan

gles

in

Tif

fan

y’s

Cle

mat

is S

kyli

ght.

Sam

ple

an

swer

:ab

ou

t 5

to 2

Rea

d t

he

Less

on

1.M

atch

eac

h d

escr

ipti

on i

n t

he

firs

t co

lum

n w

ith

a w

ord

or p

hra

se f

rom

th

e se

con

dco

lum

n.

a.T

he

rati

o of

tw

o co

rres

pon

din

g qu

anti

ties

ivi.

prop

orti

on

b.

ran

d u

in t

he

equ

atio

n �r s�

�� ut �

vii

.cro

ss p

rodu

cts

c.a

com

pari

son

of

two

quan

titi

esvi

iii.

mea

ns

d.

ruan

d st

in t

he

equ

atio

n �r s�

�� ut �

iiiv

.sc

ale

fact

or

e.an

equ

atio

n s

tati

ng

that

tw

o ra

tios

are

equ

ali

v.ex

trem

es

f.s

and

tin

th

e eq

uat

ion

�r s��

� ut �iii

vi.r

atio

2.If

m,n

,p,a

nd

qar

e n

onze

ro n

um

bers

su

ch t

hat

�m n��

�p q� ,w

hic

h o

f th

e fo

llow

ing

stat

emen

ts c

ould

be

fals

e?B

,C,E

A.

np

�m

qB

.�np �

�� mq �

C.

mp

�n

qD

.qm

�pn

E.

�m n��

� pq �F.

� pq ��

� mn �

G.m

:p�

n:q

H.m

:n�

p:q

3.W

rite

tw

o pr

opor

tion

s th

at m

atch

eac

h d

escr

ipti

on.

a.M

ean

s ar

e 5

and

8;ex

trem

es a

re 4

an

d 10

.

any

two

of

�4 5��

� 18 0�,�

4 8��

� 15 0�,�

1 50 ��

�8 4� ,�1 80 �

��5 4�

b.

Mea

ns

are

5 an

d 4;

extr

emes

are

pos

itiv

e in

tege

rs t

hat

are

dif

fere

nt

from

mea

ns.

any

two

of

�2 5��

� 14 0�,�

2 4��

� 15 0�,�

1 4��

� 25 0�,�

1 5��

� 24 0�,�

1 50 ��

�4 2� ,�1 40 �

��5 2� ,

�2 40 ��

�5 1� ,

or

�2 50 ��

�4 1�

Rem

emb

er W

hat

Yo

u L

earn

ed

4.S

omet

imes

it

is e

asie

r to

rem

embe

r a

mat

hem

atic

al i

dea

if y

ou p

ut

it i

nto

wor

ds w

ith

out

usi

ng

any

mat

hem

atic

al s

ymbo

ls.H

ow c

an y

ou u

se t

his

app

roac

h t

o re

mem

ber

the

con

cept

of

equ

alit

y of

cro

ss p

rodu

cts?

Sam

ple

an

swer

:Th

e p

rod

uct

of

the

mea

ns

equ

als

the

pro

du

ct o

f th

e ex

trem

es.

Lesson 7-1

Cha

pter

73

Gle

ncoe

Geo

met

ry


Ant

icip

atio

n G

uide

Pro

po

rtio

ns

and

Sim

ilari

ty

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7

Bef

ore

you

beg

in C

ha

pte

r 7

•R

ead

each

sta

tem

ent.

•D

ecid

e w

het

her

you

Agr

ee (

A)

or D

isag

ree

(D)

wit

h t

he

stat

emen

t.

•W

rite

A o

r D

in

th

e fi

rst

colu

mn

OR

if

you

are

not

su

re w

het

her

you

agr

ee o

rdi

sagr

ee,w

rite

NS

(N

ot S

ure

).

Aft

er y

ou c

omp

lete

Ch

ap

ter

7

•R

erea

d ea

ch s

tate

men

t an

d co

mpl

ete

the

last

col

um

n b

y en

teri

ng

an A

or

a D

.

•D

id a

ny

of y

our

opin

ion

s ab

out

the

stat

emen

ts c

han

ge f

rom

th

e fi

rst

colu

mn

?

•F

or t

hos

e st

atem

ents

th

at y

ou m

ark

wit

h a

D,u

se a

pie

ce o

f pa

per

to w

rite

an

exam

ple

of w

hy

you

dis

agre

e.

STEP

1

STEP

2

ST

EP

1S

tate

men

tS

TE

P 2

A,D

,or

NS

A o

r D

1.R

atio

s ar

e al

way

s w

ritt

en a

s fr

acti

ons.

D2.

A p

ropo

rtio

n i

s an

equ

atio

n s

tati

ng

that

tw

o ra

tios

are

eq

ual

.A

3.T

wo

rati

os a

re i

n p

ropo

rtio

n t

o ea

ch o

ther

on

ly i

f th

eir

cros

s pr

odu

cts

are

equ

al.

A

4.If

�a b��

� dc � ,th

en �a c�

��d b� .

D

5.T

he

rati

o of

th

e le

ngt

hs

of t

he

side

s of

sim

ilar

fig

ure

s is

ca

lled

th

e sc

ale

fact

or f

or t

he

two

figu

res.

A

6.If

on

e an

gle

in a

tri

angl

e is

con

gru

ent

to a

n a

ngl

e in

an

oth

er t

rian

gle,

then

th

e tw

o tr

ian

gles

are

sim

ilar

.D

7.If

a li

ne is

par

alle

l to

one

side

of

a tr

iang

le a

nd in

ters

ects

th

e ot

her

two

side

s in

tw

o di

stin

ct p

oint

s,th

en t

he li

ne

sepa

rate

s th

e tw

o si

des

into

con

grue

nt s

egm

ents

.D

8.A

seg

men

t w

hos

e en

dpoi

nts

are

th

e m

idpo

ints

of

two

side

s of

a t

rian

gle

is p

aral

lel

to t

he

thir

d si

de o

f th

e tr

ian

gle.

A

9.If

tw

o tr

ian

gles

are

sim

ilar

th

en t

hei

r pe

rim

eter

s ar

e eq

ual

.D

10.

Th

e m

edia

ns

of t

wo

sim

ilar

tri

angl

es a

re i

n t

he

sam

e pr

opor

tion

as

corr

espo

ndi

ng

side

s.A

Chapter Resources

Answers (Anticipation Guide and Lesson 7–1)


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

Cha

pter

77

Gle

ncoe

Geo

met

ry


Stud

y G

uide

and

Inte

rven

tion

(co

nti

nued

)

Pro

po

rtio

ns

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-1

Use

Pro

per

ties

of

Pro

po

rtio

ns

A s

tate

men

t th

at t

wo

rati

os a

re e

qual

is

call

ed a

pro

por

tion

.In

th

e pr

opor

tion

�a b��

� dc � ,w

her

e b

and

dar

e n

ot z

ero,

the

valu

es a

and

dar

e th

e ex

trem

esan

d th

e va

lues

ban

d c

are

the

mea

ns.

In a

pro

port

ion

,th

e pr

odu

ct o

f th

em

ean

s is

equ

al t

o th

e pr

odu

ct o

f th

e ex

trem

es,s

o ad

�bc

.

�a b��

� dc �

a�

d�

b�

c↑

↑ex

trem

esm

eans

Sol

ve � 19 6�

��2 x7 �

.

� 19 6��

�2 x7 �

9 �

x�

16 �

27C

ross

pro

duct

s

9x�

432

Mul

tiply

.

x�

48D

ivid

e ea

ch s

ide

by 9

.

A r

oom

is

49 c

enti

met

ers

by

28 c

enti

met

ers

on a

sca

le

dra

win

g of

a h

ouse

.For

th

e ac

tual

roo

m,t

he

larg

er d

imen

sion

is

14 f

eet.

Fin

d t

he

shor

ter

dim

ensi

on o

f th

e ac

tual

roo

m.

If x

is t

he

room

’s s

hor

ter

dim

ensi

on,t

hen

�2 48 9��

� 1x 4�

49x

�39

2C

ross

pro

duct

s

x�

8D

ivid

e ea

ch s

ide

by 4

9.

Th

e sh

orte

r si

de o

f th

e ro

om i

s 8

feet

.

Sol

ve e

ach

pro

por

tion

.

1.�1 2�

��2 x8 �

562.

�3 8��

� 2y 4�9

3.�x x� �

2 22�

��3 10 0�

8

4.� 18

3 .2��

�9 y�54

.65.

�2x8�

3�

��5 4�

3.5

6.�x x

� �1 1

��

�3 4��

7

Use

a p

rop

orti

on t

o so

lve

each

pro

ble

m.

7.If

3 c

asse

ttes

cos

t $4

4.85

,fin

d th

e co

st o

f on

e ca

sset

te.

$14.

95

8.T

he

rati

o of

th

e si

des

of a

tri

angl

e ar

e 8:

15:1

7.If

th

e pe

rim

eter

of

the

tria

ngl

e is

48

0 in

ches

,fin

d th

e le

ngt

h o

f ea

ch s

ide

of t

he

tria

ngl

e.96

in.,

180

in.,

204

in.

9.T

he

scal

e on

a m

ap i

ndi

cate

s th

at o

ne

inch

equ

als

4 m

iles

.If

two

tow

ns

are

3.5

inch

esap

art

on t

he

map

,wh

at i

s th

e ac

tual

dis

tan

ce b

etw

een

th

e to

wn

s?14

mi

shor

ter

dim

ensi

on�

��

long

er d

imen

sion

Exam

ple

1

Exam

ple

2

Exer

cise

s

Lesson 7-1

Cha

pter

76

Gle

ncoe

Geo

met

ry

Stud

y G

uide

and

Inte

rven

tion

Pro

po

rtio

ns

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Wri

te R

atio

sA

rat

iois

a c

ompa

riso

n o

f tw

o qu

anti

ties

.Th

e ra

tio

ato

b,w

her

e b

is n

ot

zero

,can

be

wri

tten

as

�a b�or

a:b

.Th

e ra

tio

of t

wo

quan

titi

es i

s so

met

imes

cal

led

a sc

ale

fact

or.F

or a

sca

le f

acto

r,th

e u

nit

s fo

r ea

ch q

uan

tity

are

th

e sa

me.

In 2

002,

the

Ch

icag

o C

ub

s b

aseb

all

team

won

67

gam

es o

ut

of 1

62.

Wri

te a

rat

io f

or t

he

nu

mb

er o

f ga

mes

won

to

the

tota

l n

um

ber

of

gam

es p

laye

d.

To

fin

d th

e ra

tio,

divi

de t

he

nu

mbe

r of

gam

es w

on b

y th

e to

tal

nu

mbe

r of

gam

es p

laye

d.T

he

resu

lt i

s � 16 67 2�

,wh

ich

is

abou

t 0.

41.T

he

Ch

icag

o C

ubs

won

abo

ut

41%

of

thei

r ga

mes

in

200

2.

A d

oll

hou

se t

hat

is

15 i

nch

es t

all

is a

sca

le m

odel

of

a re

al h

ouse

wit

h a

hei

ght

of 2

0 fe

et.W

hat

is

the

rati

o of

th

e h

eigh

t of

th

e d

oll

hou

se t

o th

eh

eigh

t of

th

e re

al h

ouse

?T

o st

art,

con

vert

th

e h

eigh

t of

th

e re

al h

ouse

to

inch

es.

20 f

eet

�12

in

ches

per

foo

t �

240

inch

esT

o fi

nd

the

rati

o or

sca

le f

acto

r of

th

e h

eigh

ts,d

ivid

e th

e h

eigh

t of

th

e do

ll h

ouse

by

the

hei

ght

of t

he

real

hou

se.T

he

rati

o is

15

inch

es:2

40 i

nch

es o

r 1:

16.T

he

hei

ght

of t

he

doll

hou

se i

s � 11 6�

the

hei

ght

of t

he

real

hou

se.

1.In

th

e 20

05 M

ajor

Lea

gue

base

ball

sea

son

,Ale

x R

odri

quez

hit

48

hom

e ru

ns

and

was

at

bat

605

tim

es.F

ind

the

rati

o of

hom

e ru

ns

to t

he

nu

mbe

r of

tim

es h

e w

as a

t ba

t.

� 64 08 5�

2.T

her

e ar

e 18

2 gi

rls

in t

he

soph

omor

e cl

ass

of 3

05 s

tude

nts

.Fin

d th

e ra

tio

of g

irls

to

tota

l st

ude

nts

.

�1 38 02 5�

3.T

he

len

gth

of

a re

ctan

gle

is 8

in

ches

an

d it

s w

idth

is

5 in

ches

.Fin

d th

e ra

tio

of l

engt

h

to w

idth

.

�8 5�

4.T

he

side

s of

a t

rian

gle

are

3 in

ches

,4 i

nch

es,a

nd

5 in

ches

.Fin

d th

e sc

ale

fact

or b

etw

een

the

lon

gest

an

d th

e sh

orte

st s

ides

.

�5 3�

5.T

he

len

gth

of

a m

odel

tra

in i

s 18

in

ches

.It

is a

sca

le m

odel

of

a tr

ain

th

at i

s 48

fee

t lo

ng.

Fin

d th

e sc

ale

fact

or.

� 31 2�

Exam

ple

1

Exam

ple

2

Exer

cise

s

Answers (Lesson 7–1)


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

An

swer

s

Cha

pter

79

Gle

ncoe

Geo

met

ry


Prac

tice

Pro

po

rtio

ns

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-1

1.N

UTR

ITIO

NO

ne o

unce

of

ched

dar

chee

se c

onta

ins

9 gr

ams

of f

at.S

ix o

f th

e gr

ams

of f

atar

e sa

tura

ted

fats

.Fin

d th

e ra

tio

of s

atur

ated

fat

s to

tot

al f

at i

n an

oun

ce o

f ch

eese

.

2:3

2.FA

RM

ING

Th

e ra

tio

of g

oats

to

shee

p at

a u

niv

ersi

ty r

esea

rch

far

m i

s 4:

7.T

he

nu

mbe

r of

sh

eep

at t

he

farm

is

28.W

hat

is

the

nu

mbe

r of

goa

ts?

16

3.A

RT

Edw

ard

Hop

per’

s oi

l on

can

vas

pain

tin

g N

igh

thaw

ksh

as a

len

gth

of

60 i

nch

es a

nd

a w

idth

of

30 i

nch

es.A

pri

nt

of t

he

orig

inal

has

a l

engt

h o

f 2.

5 in

ches

.Wh

at i

s th

e w

idth

of

the

prin

t?

1.25

in.

Sol

ve e

ach

pro

por

tion

.

4.�5 8�

�� 1x 2�

7.5

5.� 1.

x 12��

�1 5�0.

224

6.� 26 7x �

��4 3�

6

7.�x

� 32

��

�8 9��2 3�

8.�3x

4�5

��

�� 75 ��5 7�

9.�x

� 42

��

�x� 2

4�

�10

Fin

d t

he

mea

sure

s of

th

e si

des

of

each

tri

angl

e.

10.T

he

rati

o of

th

e m

easu

res

of t

he

side

s of

a t

rian

gle

is 3

:4:6

,an

d it

s pe

rim

eter

is

104

feet

.

24 f

t,32

ft,

48 f

t

11.T

he r

atio

of

the

mea

sure

s of

the

sid

es o

f a

tria

ngle

is 7

:9:1

2,an

d it

s pe

rim

eter

is 8

4 in

ches

.

21 in

.,27

in.,

36 in

.

12.T

he

rati

o of

th

e m

easu

res

of t

he

side

s of

a t

rian

gle

is 6

:7:9

,an

d it

s pe

rim

eter

is

77 c

enti

met

ers.

21 c

m,2

4.5

cm,3

1.5

cm

Fin

d t

he

mea

sure

s of

th

e an

gles

in

eac

h t

rian

gle.

13.T

he

rati

o of

th

e m

easu

res

of t

he

angl

es i

s 4:

5:6.

48,6

0,72

14.T

he

rati

o of

th

e m

easu

res

of t

he

angl

es i

s 5:

7:8.

45,6

3,72

15.B

RID

GES

Th

e sp

an o

f th

e B

enja

min

Fra

nkl

in s

usp

ensi

on b

ridg

e in

Ph

ilad

elph

ia,

Pen

nsy

lvan

ia,i

s 17

50 f

eet.

A m

odel

of

the

brid

ge h

as a

spa

n o

f 42

in

ches

.Wh

at i

s th

era

tio

of t

he

span

of

the

mod

el t

o th

e sp

an o

f th

e ac

tual

Ben

jam

in F

ran

klin

Bri

dge?

� 51 00�

Lesson 7-1

Cha

pter

78

Gle

ncoe

Geo

met

ry

Skill

s Pr

acti

ceP

rop

ort

ion

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-1


1.FO

OTB

ALL

A t

igh

t en

d sc

ored

6 t

ouch

dow

ns

in 1

4 ga

mes

.Fin

d th

e ra

tio

of t

ouch

dow

ns

per

gam

e.

0.43

:1

2.E

DU

CA

TIO

NIn

a s

ched

ule

of

6 cl

asse

s,M

arta

has

2 e

lect

ive

clas

ses.

Wh

at i

s th

e ra

tio

of e

lect

ive

to n

on-e

lect

ive

clas

ses

in M

arta

’s s

ched

ule

?

1:2

3.B

IOLO

GY

Ou

t of

274

lis

ted

spec

ies

of b

irds

in

th

e U

nit

ed S

tate

s,78

spe

cies

mad

e th

een

dan

gere

d li

st.F

ind

the

rati

o of

en

dan

gere

d sp

ecie

s of

bir

ds t

o li

sted

spe

cies

in

th

eU

nit

ed S

tate

s.

� 13 39 7�

4.A

RT

An

art

ist

in P

ortl

and,

Ore

gon

,mak

es b

ron

ze s

culp

ture

s of

dog

s.T

he

rati

o of

th

eh

eigh

t of

a s

culp

ture

to

the

actu

al h

eigh

t of

th

e do

g is

2:3

.If

the

hei

ght

of t

he

scu

lptu

reis

14

inch

es,f

ind

the

hei

ght

of t

he

dog.

21 in

.

5.SC

HO

OL

Th

e ra

tio

of m

ale

stu

den

ts t

o fe

mal

e st

ude

nts

in

th

e dr

ama

clu

b at

Cam

pbel

lH

igh

Sch

ool

is 3

:4.I

f th

e n

um

ber

of m

ale

stu

den

ts i

n t

he

clu

b is

18,

wh

at i

s th

e n

um

ber

of f

emal

e st

ude

nts

?

24

Sol

ve e

ach

pro

por

tion

.

6.�2 5�

�� 4x 0�

167.

� 17 0��

�2 x1 �30

8.�2 50 �

��4 6x �

6

9.�5 4x �

��3 85 �

3.5

10.�

x� 3

1�

��7 2�

9.5

11.�

1 35 ��

�x� 5

3�

28

Fin

d t

he

mea

sure

s of

th

e si

des

of

each

tri

angl

e.

12.T

he

rati

o of

th

e m

easu

res

of t

he

side

s of

a t

rian

gle

is 3

:5:7

,an

d it

s pe

rim

eter

is

450

cen

tim

eter

s.90

cm

,150

cm

,210

cm

13.T

he r

atio

of

the

mea

sure

s of

the

sid

es o

f a

tria

ngle

is 5

:6:9

,and

its

peri

met

er is

220

met

ers.

55 m

,66

m,9

9 m

14.T

he

rati

o of

th

e m

easu

res

of t

he

side

s of

a t

rian

gle

is 4

:6:8

,an

d it

s pe

rim

eter

is

126

feet

.28

ft,

42 f

t,56

ft

15.T

he r

atio

of

the

mea

sure

s of

the

sid

es o

f a

tria

ngle

is

5:7:

8,an

d it

s pe

rim

eter

is

40 i

nche

s.10

in.,

14 in

.,16

in.



Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

Cha

pter

711

Gle

ncoe

Geo

met

ry


Enri

chm

ent

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-1

Gro

wth

Ch

arts

It i

s sa

id t

hat

wh

en a

ch

ild

has

rea

ched

th

e ag

e of

2 y

ears

,he

is r

ough

ly h

alf

of h

isad

ult

hei

ght.

Th

e gr

owth

ch

art

belo

w s

how

s th

e gr

owth

acc

ordi

ng

to p

erce

nti

les

for

boys

.

1.U

se t

he

char

t to

det

erm

ine

the

appr

oxim

ate

hei

ght

for

a bo

y at

age

2 i

f h

e is

in

the

75th

to

95th

per

cen

tile

.

35–

37 in

ches

2.U

sin

g th

e ru

le t

hat

th

e h

eigh

t at

age

2 i

s ap

prox

imat

ely

hal

f of

his

adu

lt h

eigh

t,se

t u

p a

prop

orti

on t

o so

lve

for

the

adu

lt h

eigh

t of

th

e bo

y in

exe

rcis

e 1.

Sol

veyo

ur

prop

orti

on.

�3 x6 ��

�1 2� ;72

inch

es

3.U

se t

he

char

t to

app

roxi

mat

e th

e h

eigh

t at

age

18

for

a bo

y if

he

is i

n t

he

75th

to 9

5th

per

cen

tile

.How

doe

s th

is a

nsw

er c

ompa

re t

o th

e an

swer

to

prob

lem

1?

72–

74 in

ches

:th

e tw

o a

nsw

ers

are

very

clo

se

4.R

epea

t th

is p

roce

ss f

or a

boy

wh

o is

in

th

e 5t

h t

o 25

th p

erce

nti

le.

32–

34 in

ches

;64

inch

es;

65–

68 in

ches

5.Is

usi

ng

the

rule

th

at a

boy

is

hal

f of

his

adu

lt h

eigh

t at

age

2 y

ears

a g

ood

appr

oxim

atio

n?

Exp

lain

.

Yes,

it a

pp

ears

to

be

a g

oo

d a

pp

roxi

mat

ion

.

85 75 65 55 45 35

24

68

1012

1416

18

Ag

e (y

r)

Height (in.)

Perc

enti

le G

rou

p

5th

to

25t

h

25th

to

75t

h

75th

to

95t

h

A B

Lesson 7-1

1.M

OD

ELS

Lu

ke w

ants

to

mak

e a

scal

em

odel

of

a B

oein

g 74

7 je

tlin

er.H

e w

ants

ever

y fo

ot o

f h

is m

odel

to

repr

esen

t 50

feet

.Com

plet

e th

e fo

llow

ing

tabl

e.

(Sou

rce:

ww

w.b

oein

g.co

m)

2.R

ATI

ON

SS

ixte

en s

tude

nts

wen

t on

a

wee

k-lo

ng

hik

ing

trip

.Th

ey b

rou

ght

wit

h t

hem

320

spe

cial

ly b

aked

,pro

tein

-ri

ch,c

ooki

es.W

hat

is

the

rati

o of

coo

kies

to s

tude

nts

?20

:1

3.PH

OTO

GR

APH

ST

racy

is

4 fe

et

tall

an

d h

er f

ath

er i

s 6

feet

tal

l.In

a

phot

ogra

ph o

f th

e tw

o of

th

emst

andi

ng

side

by

side

,Tra

cy’s

im

age

is 2

in

ches

tal

l.

Alt

hou

gh t

hei

r im

ages

are

mu

ch s

mal

ler,

the

rati

o of

th

eir

hei

ghts

rem

ain

s th

esa

me.

How

tal

l is

Tra

cy’s

fat

her

’s i

mag

ein

th

e ph

oto?

3 in

.

4.C

AR

SA

car

com

pan

y bu

ilds

tw

ove

rsio

ns

of o

ne

of i

ts m

odel

s—a

seda

nan

d a

stat

ion

wag

on.T

he

rati

o of

sed

ans

to s

tati

on w

agon

s is

11

:2.A

fre

igh

ter

begi

ns

un

load

ing

the

cars

at

a do

ck.

Tom

cou

nts

18

stat

ion

wag

ons

and

then

over

hea

rs a

doc

k w

orke

r ca

ll o

ut,

“Oka

y,th

at’s

all

of

the

wag

ons

...b

rin

g ou

t th

e se

dan

s!”

How

man

y se

dan

s w

ere

onth

e sh

ip?

99

MA

PSF

or E

xerc

ises

5–7

,use

th

efo

llow

ing

info

rmat

ion

.C

arlo

s m

akes

a m

ap o

f h

is n

eigh

borh

ood

for

a pr

esen

tati

on.T

he

scal

e of

his

map

is

1 in

ch :

125

feet

.

5.H

ow m

any

feet

do

4 in

ches

rep

rese

nt

onth

e m

ap?

500

ft

6.C

arlo

s li

ves

250

feet

aw

ay f

rom

An

drew

.H

ow m

any

inch

es s

epar

ate

Car

los’

hom

efr

om A

ndr

ew’s

on

th

e m

ap?

2 in

.

7.D

uri

ng

a pr

acti

ce r

un

in

fro

nt

of h

ispa

ren

ts,C

arlo

s re

aliz

es t

hat

his

map

is

far

too

sm

all.

He

deci

des

to m

ake

his

map

5 t

imes

as

larg

e.W

hat

wou

ld

be t

he

scal

e of

th

e la

rger

map

?1

in.:

25 f

t

6 ft

4 ft

Cha

pter

710

Gle

ncoe

Geo

met

ry

Wor

d Pr

oble

m P

ract

ice

Pro

po

rtio

ns

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-1


Act

ual

Mo

del

Par

tle

ng

th (

in.)

len

gth

(in

.)

Win

g S

pan

2,53

750

.74

Leng

th2,

782

55.6

4Ta

il H

eigh

t39

27.

84



Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

An

swer

s

Cha

pter

713

Gle

ncoe

Geo

met

ry


Less

on R

eadi

ng G

uide

Sim

ilar

Po

lyg

on

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-2

Get

Rea

dy

for

the

Less

on

Rea

d t

he

intr

odu

ctio

n t

o L

esso

n 7

-2 i

n y

our

text

boo

k.

•D

escr

ibe

the

figu

res

that

hav

e si

mil

ar s

hap

es. S

amp

le a

nsw

er:

Lig

ht

and

dar

kfi

gu

res

are

arra

ng

ed in

alt

ern

atin

g p

atte

rns.

Fig

ure

s th

at h

ave

thei

r fe

etp

oin

tin

g t

ow

ard

th

e ce

nte

r o

f th

e ci

rcle

hav

e th

e sa

me

shap

e bu

t d

iffe

ren

tsi

zes.

•W

hat

hap

pen

s to

th

e fi

gure

s as

you

r ey

es m

ove

from

th

e ce

nte

r to

th

e ou

ter

edge

?S

amp

le a

nsw

er:T

he

fig

ure

s b

eco

me

smal

ler.

Rea

d t

he

Less

on

1.C

ompl

ete

each

sen

ten

ce.

a.T

wo

poly

gon

s th

at h

ave

exac

tly

the

sam

e sh

ape,

but

not

nec

essa

rily

th

e sa

me

size

,ar

e .

b.

Tw

o po

lygo

ns

are

con

gru

ent

if t

hey

hav

e ex

actl

y th

e sa

me

shap

e an

d th

e sa

me

.c.

Tw

o po

lygo

ns

are

sim

ilar

if

thei

r co

rres

pon

din

g an

gles

are

an

d th

eir

corr

espo

ndi

ng

side

s ar

e .

d.

Tw

o po

lygo

ns

are

con

gru

ent

if t

hei

r co

rres

pon

din

g an

gles

are

an

d th

eir

corr

espo

ndi

ng

side

s ar

e .

e.T

he

rati

o of

th

e le

ngt

hs

of c

orre

spon

din

g si

des

of t

wo

sim

ilar

fig

ure

s is

cal

led

the

.f.

Mu

ltip

lyin

g th

e co

ordi

nat

es o

f al

l po

ints

of

a fi

gure

in

th

e co

ordi

nat

e pl

ane

by a

sca

le

fact

or t

o ge

t a

sim

ilar

fig

ure

is

call

ed a

.

g.If

tw

o po

lygo

ns a

re s

imila

r w

ith

a sc

ale

fact

or o

f 1,

then

the

pol

ygon

s ar

e .

2.D

eter

min

e w

het

her

eac

h s

tate

men

t is

alw

ays,

som

etim

es,o

r n

ever

tru

e.a.

Tw

o si

mil

ar t

rian

gles

are

con

gru

ent.

som

etim

esb

.T

wo

equ

ilat

eral

tri

angl

es a

re c

ongr

uen

t.so

met

imes

c.A

n e

quil

ater

al t

rian

gle

is s

imil

ar t

o a

scal

ene

tria

ngl

e.n

ever

d.

Tw

o re

ctan

gles

are

sim

ilar

.so

met

imes

e.T

wo

isos

cele

s ri

ght

tria

ngl

es a

re c

ongr

uen

t.so

met

imes

f.T

wo

isos

cele

s ri

ght

tria

ngl

es a

re s

imil

ar.

alw

ays

g.A

squ

are

is s

imil

ar t

o an

equ

ilat

eral

tri

angl

e.n

ever

h.

Tw

o ac

ute

tri

angl

es a

re s

imil

ar.

som

etim

esi.

Tw

o re

ctan

gles

in

wh

ich

th

e le

ngt

h i

s tw

ice

the

wid

th a

re s

imil

ar.

alw

ays

j.T

wo

con

gru

ent

poly

gon

s ar

e si

mil

ar.

alw

ays

Rem

emb

er W

hat

Yo

u L

earn

ed3.

A g

ood

way

to

rem

embe

r a

new

mat

hem

atic

al v

ocab

ula

ry t

erm

is

to r

elat

e it

to

wor

dsu

sed

in e

very

day

life

.Th

e w

ord

scal

eh

as m

any

mea

nin

gs i

n E

ngl

ish

.Giv

e th

ree

phra

ses

that

in

clu

de t

he

wor

d sc

ale

in a

way

th

at i

s re

late

d to

pro

port

ion

s.S

amp

le a

nsw

er:

scal

e d

raw

ing

,sca

le m

od

el,s

cale

of

mile

s (o

n a

map

)

con

gru

ent

dila

tio

n

scal

e fa

cto

r

con

gru

ent

con

gru

ent

pro

po

rtio

nal

con

gru

ent

sizesi

mila

r

Lesson 7-2

Cha

pter

712

Gle

ncoe

Geo

met

ry

Gra

phin

g Ca

lcul

ator

Act

ivit

yS

olv

ing

Pro

po

rtio

ns

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-1


You

can

use

a c

alcu

lato

r to

sol

ve p

ropo

rtio

ns.

Sol

ve t

he

pro

por

tion

by

usi

ng

cros

s p

rod

uct

s.

�5 15 6. .6 9��

�45x.8 �

Mu

ltip

ly 1

6.9

by 4

5.8.

Div

ide

the

prod

uct

by

55.6

.

En

ter:

16.9

45

.8

55.6

13

.92

122

30

2

Th

e so

luti

on is

app

roxi

mat

ely

13.9

21.

Sol

ve e

ach

pro

por

tion

by

usi

ng

cros

s p

rod

uct

s.R

oun

d y

our

answ

ers

to t

he

nea

rest

hu

nd

red

th.

1.�1 33 9. .9 8�

��1

0 x.5 �2.

�2 35 7. .9 7��

�24x.3 �

3.�1 59 4. .6 3�

��27

x.7 �

x�

30.0

6x

�35

.37

x�

76.7

4

4.�6 46 3. .8 4�

�� 16

x .9�5.

�7 35 7. .4 2��

� 32x .4�

6.� 46

x .2��

�2 39 6. .7 4�

x �

26.0

1x

�65

.67

x �

37.7

0

7.� 14

x .9��

�1 26 4. .8 6�8.

�35x.8 �

�

�3 22 7. .9 8�9.

�46x.9 �

��1 95 9. .7 9�

x�

10.1

8x

�30

.25

x�

298.

43

10.

�3 24 1. .9 1��

� 36x .6�

11.

� 99x .8�

��3 42 5. .2 3�

12.

�68x.9 �

��4 84 6. .3 4�

x�

60.5

4x

�70

.94

x�

134.

38

EN

TER

��

Exam

ple

Answers (Lessons 7–1 and 7–2)


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

Cha

pter

715

Gle

ncoe

Geo

met

ry


Stud

y G

uide

and

Inte

rven

tion

(co

nti

nued

)

Sim

ilar

Po

lyg

on

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-2

Scal

e Fa

cto

rsW

hen

tw

o po

lygo

ns

are

sim

ilar

,th

e ra

tio

of t

he

len

gth

s of

cor

resp

ondi

ng

side

s is

cal

led

the

scal

e fa

ctor

.At

the

righ

t,�

AB

C�

�X

YZ

.Th

e sc

ale

fact

or o

f �

AB

Cto

�X

YZ

is 2

an

d th

e sc

ale

fact

or o

f

�X

YZ

to �

AB

Cis

�1 2� .3

cm

6 cm

8 cm

10 c

m5

cm4

cm ZY

XCA

B

Th

e tw

o p

olyg

ons

are

sim

ilar

.Fin

d x

and

y.

Use

th

e co

ngr

uen

t an

gles

to

wri

te t

he

corr

espo

ndi

ng

vert

ices

in

ord

er.

�R

ST

��

MN

PW

rite

pro

port

ion

s to

fin

d x

and

y.

�3 12 6��

� 1x 3��3 y8 �

��3 12 6�

16x

�32

(13)

32y

�38

(16)

x�

26y

�19

x

y38

3216

13T

S

RP

N

M

�A

BC

��

CD

E.F

ind

th

e sc

ale

fact

or a

nd

fin

d t

he

len

gth

s of

C �D�

and

D�E�

.

AC

�3

�0

�3

and

CE

�9

�3

�6.

Th

esc

ale

fact

or o

f �

CD

Eto

�A

BC

is 6

:3 o

r 2:

1.U

sin

g th

e D

ista

nce

For

mu

la,

AB

��

1 �

9�

��

10�an

d B

C�

�4

�9

��

�13�

.Th

e le

ngt

hs

of t

he

side

s of

�C

DE

are

twic

e th

ose

of �

AB

C,

so D

C�

2(B

A)

or 2

�10�

and

DE

�2(

BC

) or

2�

13�.

x

y

A( 0

, 0)

B( 1

, 3) C( 3

, 0)

E( 9

, 0)

D

Eac

h p

air

of p

olyg

ons

is s

imil

ar.F

ind

xan

d y

.

1.2.

x�

6;y

�15

x�

2.25

;y

�5

3.4.

x�

27;

y�

15x

�24

;y

�27

5.In

Exa

mpl

e 2

abov

e,po

int

Dh

as c

oord

inat

es (

5,6)

.Use

th

e D

ista

nce

For

mu

la t

o ve

rify

the

len

gth

s of

C �D�

and

D�E�

.

CD

�2�

10�,D

E�

2�13�

40

36x

30

18y

12

y �

1

18

24

x18

10y

4.5

x2.

5 5

9

12y8 10

x

Exam

ple

1Ex

amp

le 2

Exer

cise

s

Lesson 7-2

Cha

pter

714

Gle

ncoe

Geo

met

ry

Stud

y G

uide

and

Inte

rven

tion

Sim

ilar

Po

lyg

on

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-2


Iden

tify

Sim

ilar

Fig

ure

s

Det

erm

ine

wh

eth

er t

he

tria

ngl

es

are

sim

ilar

.T

wo

poly

gon

s ar

e si

mil

ar i

f an

d on

ly i

f th

eir

corr

espo

ndi

ng

angl

es a

re c

ongr

uen

t an

d th

eir

corr

espo

ndi

ng

side

s ar

e pr

opor

tion

al.

�C

��

Zbe

cau

se t

hey

are

rig

ht

angl

es,a

nd

�B

��

X.

By

the

Th

ird

An

gle

Th

eore

m,�

A�

�Y

.

For

th

e si

des,

�B XC Z�

��2 20 3�

,�B X

A Y��

��2 20 3�

,an

d �A Y

C Z��

�2 20 3�.

Th

e si

de l

engt

hs

are

prop

orti

onal

.So

�B

CA

��

XZ

Y.

Is p

olyg

on W

XY

Z�

pol

ygon

PQ

RS

?

For

th

e si

des,

�W PQX �

��1 82 �

��3 2� ,

� QXY R�

��1 18 2�

��3 2� ,

� RYZ S�

��1 15 0�

��3 2� ,

and

�Z SW P��

�9 6��

�3 2� .S

o co

rres

pon

din

g si

des

are

prop

orti

onal

.

Als

o,�

W�

�P

,�X

��

Q,�

Y�

�R

,an

d �

Z�

�S

,so

corr

espo

ndi

ng

angl

es a

re c

ongr

uen

t.W

e ca

n c

oncl

ude

th

at

poly

gon

WX

YZ

�po

lygo

n P

QR

S.

Det

erm

ine

wh

eth

er e

ach

pai

r of

fig

ure

s is

sim

ilar

.If

they

are

sim

ilar

,giv

e th

era

tio

of c

orre

spon

din

g si

des

.

1.2.

yes;

�5 8�n

o

3.4.

yes;

�1 2�ye

s;�5 4�

10y

8y

37�

37�

116�

27�

5 x

4x15

z12

z

2211

1610 equi

late

ral t

riang

les

15

9

12

18XW

ZY

10

6

8

12

QP S

R

20�

2�� 23

�2�

2023

2320

20�

�223

��2

45�

45�

CA

XZ

BY

Exam

ple

1

Exam

ple

2

Exer

cise

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.

An

swer

s

Cha

pter

717

Gle

ncoe

Geo

met

ry


Prac

tice

Sim

ilar

Po

lyg

on

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-2

Det

erm

ine

wh

eth

er e

ach

pai

r of

fig

ure

s is

sim

ilar

.Ju

stif

y yo

ur

answ

er.

1.2.

JKL

M�

QR

SP

;�

AB

C�

�U

VT

;�

A�

�U

,�

J�

�Q

,�K

��

R,

�B

��

V,a

nd

�C

��

Tby

th

e �

L�

�S

,�M

��

P,a

nd

T

hir

d A

ng

le T

heo

rem

an

d

� QJKR�

�� RK

SL ��

�L SM P��

� PMQJ �

��5 3�

or

1.67

�A UB V�

��B V

C T��

�C TUA �

��2 3� .

Eac

h p

air

of p

olyg

ons

is s

imil

ar.W

rite

a s

imil

arit

y st

atem

ent,

and

fin

d x

,th

em

easu

re(s

) of

th

e in

dic

ated

sid

e(s)

,an

d t

he

scal

e fa

ctor

.

3.L �

M�an

d M�

N�4.

D�E�

and

D�F�

AB

CD

�L

MN

P;

�A

BC

��

DE

F;

�3 2� ;10

�1 2� ;7�

1 2� ;�4 3�

7;4;

8;�3 2�

5.C

OO

RD

INA

TE G

EOM

ETRY

Tri

angl

e A

BC

has

ver

tice

s A

(0,0

),B

(�4,

0),a

nd

C(�

2,4)

.T

he

coor

din

ates

of

each

ver

tex

are

mu

ltip

lied

by

3 to

cre

ate

�A

EF

.Sh

ow t

hat

�A

EF

issi

mil

ar t

o �

AB

C.

AB

�4,

BC

�C

A�

2�5�

and

AE

�12

,EF

�FA

�6�

5�.�A A

B E��

�B EC F�

��C FA

A ��

�1 3� ;�

A�

�A

and

sin

ce B�

C�|| E�

F�,�

B�

�E

and

�C

��

F.S

ince

th

e co

rres

po

nd

ing

an

gle

s ar

e co

ng

ruen

t an

d t

he

corr

esp

on

din

g s

ides

are

pro

po

rtio

nal

,�A

BC

��

AE

F.

6.IN

TER

IOR

DES

IGN

Gra

ham

use

d th

e sc

ale

draw

ing

of h

is l

ivin

g ro

om t

o de

cide

wh

ere

to p

lace

fu

rnit

ure

.Fin

d th

e di

men

sion

s of

th

eli

vin

g ro

om i

f th

e sc

ale

in t

he

draw

ing

is 1

in

ch �

4.5

feet

.18

ft

by 1

1 ft

3 in

.4

in.

21 – 2 in.

612

40�

40�

x �

1

x �

3A

F

E

D

BC

14

10

x �

6

x �

9

CN

MD

AB

LP

2412

1416

2118

VU

AC

BT

2512

9

14.4

1524

20

15

JM

QRS

PK

L

Lesson 7-2

Cha

pter

716

Gle

ncoe

Geo

met

ry

Skill

s Pr

acti

ceS

imila

r P

oly

go

ns

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-2


Det

erm

ine

wh

eth

er e

ach

pai

r of

fig

ure

s is

sim

ilar

.Ju

stif

y yo

ur

answ

er.

1.2.

�A

BC

��

DE

F;

�A

��

D,

rho

mbu

s P

QR

S�

rho

mbu

s W

XY

Z;

�C

��

F,a

nd

�B

��

E�

P�

�W

,�Q

��

X,�

R�

�Y

,b

ecau

se if

tw

o a

ng

les

of

on

e �

S�

�Z

;tr

ian

gle

are

co

ng

ruen

t to

tw

o

� WPQ X�

��Q X

YR ��

�R YS Z�

�� ZS WP �

�� 73 .5�

�0.

4an

gle

s o

f a

seco

nd

tri

ang

le,t

hen

th

e th

ird

an

gle

s ar

e co

ng

ruen

t;

�A DB E�

��B E

C F��

�C FDA �

��3 2� .

Eac

h p

air

of p

olyg

ons

is s

imil

ar.W

rite

a s

imil

arit

y st

atem

ent,

and

fin

d x

,th

em

easu

re(s

) of

th

e in

dic

ated

sid

e(s)

,an

d t

he

scal

e fa

ctor

.

3.G �

H�4.

S�T�

and

S�U�

AB

CD

�E

FG

H;

�W

XY

��

ST

U(o

r �

SU

T)

6�1 2� ;

6�1 2� ;

27;

12;

12;

�1 3�

5.W�

T�6.

T�S�

and

S�P�

PQ

RS

�U

VW

T;

�L

MN

��

TS

P;

5;6;

�3 2�13

;12

;15

;�2 3�

10

8

x �

2

x �

1

SP

MN

L

T

9

10 3

x �

1

5

P

S

RU

V

WT

Q

x �

5

x �

5

9

3

44

S

W

XY

T U2614

1213

BC

DA

1376

x G

EH

F

7.5

7.5

7.5

7.5

ZY

XW

3

3

33

SR

QP

10.5

69

59�

35�

AC

B

7

46

59�

35�

DF

E



Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

Cha

pter

719

Gle

ncoe

Geo

met

ry


Enri

chm

ent

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-2

Co

nst

ruct

ing

Sim

ilar

Po

lyg

on

sH

ere

are

fou

r st

eps

for

con

stru

ctin

g a

poly

gon

th

at i

s si

mil

ar t

o an

d w

ith

si

des

twic

e as

lon

g as

th

ose

of a

n e

xist

ing

poly

gon

.

Ste

p 1

Ch

oose

an

y po

int

eith

er i

nsi

de o

r ou

tsid

e th

e po

lygo

n a

nd

labe

l it

O.

Ste

p 2

Dra

w r

ays

from

Oth

rou

gh e

ach

ver

tex

of t

he

poly

gon

.S

tep

3F

or v

erte

x V

,set

th

e co

mpa

ss t

o le

ngt

h O

V.T

hen

loc

ate

a n

ew p

oin

tV

�on

ray

OV

such

th

at V

V�

�O

V.T

hu

s,O

V�

�2(

OV

).S

tep

4R

epea

t S

tep

3 fo

r ea

ch v

erte

x.C

onn

ect

poin

ts V

�,W

�,X

�an

d Y

�to

form

th

e n

ew p

olyg

on.

Tw

o co

nst

ruct

ion

s of

pol

ygon

s si

mil

ar t

o an

d w

ith

sid

es t

wic

e th

ose

of V

WX

Yar

e sh

own

bel

ow.N

otic

e th

at t

he

plac

emen

t of

poi

nt

Odo

es n

ot a

ffec

t th

e si

zeor

sh

ape

of V

�W�X

�Y�,

only

its

loc

atio

n.

Tra

ce e

ach

pol

ygon

.Th

en c

onst

ruct

a s

imil

ar p

olyg

on w

ith

sid

es t

wic

e as

lon

g as

thos

e of

th

e gi

ven

pol

ygon

.S

ee s

tud

ents

’co

nst

ruct

ion

s.

1.2.

DE

F

GC

A

B

VW

YX

VW

YX

V�

W�

X�

Y�

O

VW

YX

V�

W�

X�

Y�

O

3.E

xpla

in h

ow t

o co

nst

ruct

a s

imil

arpo

lygo

n w

ith

side

s th

ree

tim

es t

he l

engt

hof

th

ose

of p

olyg

on H

IJK

L.T

hen

do

the

con

stru

ctio

n.

See

stu

den

ts’w

ork

.

4.E

xpla

in h

ow t

o co

nst

ruct

a s

imil

ar

poly

gon

1�1 2�

tim

es t

he

len

gth

of

thos

e of

poly

gon

MN

PQ

RS

.Th

en d

o th

eco

nst

ruct

ion

.S

ee s

tud

ents

’wo

rk.

M

S

R

N

Q

P

HI

LK

J

Lesson 7-2

Cha

pter

718

Gle

ncoe

Geo

met

ry

Wor

d Pr

oble

m P

ract

ice

Sim

ilar

Po

lyg

on

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-2


1.PA

NEL

SW

hen

clo

sed,

an e

nte

rtai

nm

ent

cen

ter

is m

ade

of f

our

squ

are

pan

els.

Th

e th

ree

smal

ler

pan

els

are

con

gru

ent

squ

ares

.

Wh

at i

s th

e sc

ale

fact

or o

f th

e la

rger

squ

are

to o

ne

of t

he

smal

ler

squ

ares

?3

2.D

OW

NSP

OU

TSD

uri

ng

a st

orm

,on

e of

th

e do

wn

spou

ts o

n M

r.H

erre

ra’s

hou

se w

as b

roke

n a

nd

nee

ded

to b

ere

plac

ed.U

nfo

rtu

nat

ely,

the

dow

nsp

out

was

too

dam

aged

to

mea

sure

its

len

gth

and

it w

as t

oo d

iffi

cult

to

mea

sure

th

eh

eigh

t of

th

e gu

tter

.Lu

ckil

y,M

r.H

erre

rah

ad a

sca

le m

odel

of

his

hou

se.I

f th

e do

wn

spou

t in

th

e m

odel

was

1�1 2�

feet

lo

ng

and

the

scal

e fa

ctor

was

20,

how

lon

g w

as t

he

actu

al d

own

spou

t?30

ft

3.O

RIG

AM

IB

axte

r u

ses

an 8

-in

ch

squ

are

piec

e of

ori

gam

i pa

per

to m

ake

an o

riga

mi

mod

el o

f a

chic

ken

.Wh

enfi

nis

hed

,th

e ch

icke

n s

tan

ds 4

in

ches

hig

h.B

axte

r w

ants

to

mak

e an

oth

eror

igam

i ch

icke

n,o

nly

th

is t

ime

he

wan

ts t

o m

ake

it 1

2 in

ches

hig

h i

nst

ead.

Wh

at s

ize

piec

e of

pap

er s

hou

ld h

e u

seto

do

this

?2

ft s

qu

are

4.EN

LAR

GIN

GC

amil

le w

ants

to

mak

e a

patt

ern

for

a f

our-

poin

ted

star

wit

hdi

men

sion

s tw

ice

as l

ong

as t

he

one

show

n.H

elp

her

by

draw

ing

a st

ar w

ith

dim

ensi

ons

twic

e as

lon

g on

th

e gr

idbe

low

.

BIO

LOG

YF

or E

xerc

ises

5–7

,use

th

efo

llow

ing

info

rmat

ion

.A

par

amec

ium

is

a sm

all

sin

gle-

cell

orga

nis

m.T

he

para

mec

ium

mag

nif

ied

belo

wis

act

ual

ly o

ne

ten

th o

f a

mil

lim

eter

lon

g.

5.If

you

wan

t to

mak

e a

phot

ogra

ph o

f th

eor

igin

al p

aram

eciu

m s

o th

at i

ts i

mag

e is

1 ce

nti

met

er l

ong,

by w

hat

sca

le f

acto

rsh

ould

you

mag

nif

y it

?10

0

6.If

you

wan

t to

mak

e a

phot

ogra

ph o

f th

eor

igin

al p

aram

eciu

m s

o th

at i

ts i

mag

e is

15 c

enti

met

ers

lon

g,by

wh

at s

cale

fac

tor

shou

ld y

ou m

agn

ify

it?

1500

7.B

y ap

prox

imat

ely

wh

at s

cale

fac

tor

has

the

para

mec

ium

bee

n e

nla

rged

to

mak

eth

e im

age

show

n?

400



Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

An

swer

s

Cha

pter

721

Gle

ncoe

Geo

met

ry


Stud

y G

uide

and

Inte

rven

tion

Sim

ilar T

rian

gle

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-3

Iden

tify

Sim

ilar

Tria

ng

les

Her

e ar

e th

ree

way

s to

sh

ow t

hat

tw

o tr

ian

gles

are

sim

ilar

.

AA

Sim

ilari

tyTw

o an

gles

of

one

tria

ngle

are

con

grue

nt t

o tw

o an

gles

of

anot

her

tria

ngle

.

SS

S S

imila

rity

The

mea

sure

s of

the

cor

resp

ondi

ng s

ides

of

two

tria

ngle

s ar

e pr

opor

tiona

l.

SA

S S

imila

rity

The

mea

sure

s of

tw

o si

des

of o

ne t

riang

le a

re p

ropo

rtio

nal t

o th

e m

easu

res

of

two

corr

espo

ndin

g si

des

of a

noth

er t

riang

le,

and

the

incl

uded

ang

les

are

cong

ruen

t.

Det

erm

ine

wh

eth

er t

he

tria

ngl

es a

re s

imil

ar.

� DAC F�

��6 9�

��2 3�

�B EC F�

�� 18 2�

��2 3�

� DAB E�

��1 10 5�

��2 3�

�A

BC

��

DE

Fby

SS

S S

imil

arit

y.

15

129

DE

F

10

86

AB

C

Det

erm

ine

wh

eth

er t

he

tria

ngl

es a

re s

imil

ar.

�3 4��

�6 8� ,so

�M QRN �

��N R

SP �.

m�

N�

m�

R,s

o �

N�

�R

.�

NM

P�

�R

QS

by S

AS

Sim

ilar

ity.

8

4 70�Q

RS

6

3 70�

M

NP

Det

erm

ine

wh

eth

er e

ach

pai

r of

tri

angl

es i

s si

mil

ar.J

ust

ify

you

r an

swer

.

1.2.

yes;

AA

Sim

ilari

tyn

o;

�3 26 4��

�2 10 8�

3.4.

yes;

AA

Sim

ilari

tyye

s;S

AS

Sim

ilari

ty

5.6.

yes;

SA

S S

imila

rity

yes;

SS

S S

imila

rity

32

20

1540

2524

3926

1624

18

8 65�

9

4 65�

36

2018

24

Exam

ple

1Ex

amp

le 2

Exer

cise

s

Lesson 7-3

Cha

pter

720

Gle

ncoe

Geo

met

ry

Less

on R

eadi

ng G

uide

Sim

ilar T

rian

gle

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-3


Get

Rea

dy

for

the

Less

on

Rea

d t

he

intr

odu

ctio

n t

o L

esso

n 7

-3 i

n y

our

text

boo

k.

•W

hat

doe

s it

mea

n t

o sa

y th

at t

rian

gula

r sh

apes

res

ult

in

rig

id c

onst

ruct

ion

?S

amp

le a

nsw

er:

A t

rian

gu

lar

stru

ctu

re w

ill n

ot

chan

ge

its

shap

e o

rsi

ze if

yo

u p

ush

on

its

sid

es w

ith

ou

t b

reak

ing

or

ben

din

g t

hem

.•

Wh

at w

ould

hap

pen

if

the

shap

es u

sed

in t

he

con

stru

ctio

n w

ere

quad

rila

tera

ls?

Sam

ple

an

swer

:Th

e st

ruct

ure

mig

ht

colla

pse

,bec

ause

qu

adri

late

rals

are

no

t ri

gid

.

Rea

d t

he

Less

on

1.S

tate

wh

eth

er e

ach

con

diti

on g

uar

ante

es t

hat

tw

o tr

ian

gles

are

con

gru

ent

or s

imil

ar.

If t

he

con

diti

on g

uar

ante

es t

hat

th

e tr

ian

gles

are

bot

h s

imil

ar a

nd

con

gru

ent,

wri

teco

ngr

uen

t.If

th

ere

is n

ot e

nou

gh i

nfo

rmat

ion

to

guar

ante

e th

at t

he

tria

ngl

es w

ill

beco

ngr

uen

t or

sim

ilar

,wri

te n

eith

er.

a.T

wo

side

s an

d th

e in

clu

ded

angl

e of

on

e tr

ian

gle

are

con

gru

ent

to t

wo

side

s an

d th

ein

clu

ded

angl

e of

th

e ot

her

tri

angl

e.co

ng

ruen

tb

.T

he

mea

sure

s of

all

th

ree

pair

s of

cor

resp

ondi

ng

side

s ar

e pr

opor

tion

al.

sim

ilar

c.T

wo

angl

es o

f on

e tr

ian

gle

are

con

gru

ent

to t

wo

angl

es o

f th

e ot

her

tri

angl

e.si

mila

rd

.T

wo

angl

es a

nd

a n

onin

clu

ded

side

of

one

tria

ngl

e ar

e co

ngr

uen

t to

tw

o an

gles

an

dth

e co

rres

pon

din

g n

onin

clu

ded

side

of

the

oth

er t

rian

gle.

con

gru

ent

e.T

he

mea

sure

s of

tw

o si

des

of a

tri

angl

e ar

e pr

opor

tion

al t

o th

e m

easu

res

of t

wo

corr

espo

ndi

ng

side

s of

an

oth

er t

rian

gle,

and

the

incl

ude

d an

gles

are

con

gru

ent.

sim

ilar

f.T

he

thre

e si

des

of o

ne

tria

ngl

e ar

e co

ngr

uen

t to

th

e th

ree

side

s of

th

e ot

her

tri

angl

e.co

ng

ruen

tg.

The

thr

ee a

ngle

s of

one

tri

angl

e ar

e co

ngru

ent

to t

he t

hree

ang

les

of t

he o

ther

tri

angl

e.si

mila

rh

.O

ne

acu

te a

ngl

e of

a r

igh

t tr

ian

gle

is c

ongr

uen

t to

on

e ac

ute

an

gle

of a

not

her

rig

ht

tria

ngl

e.si

mila

ri.

Th

e m

easu

res

of t

wo

side

s of

a t

rian

gle

are

prop

orti

onal

to

the

mea

sure

s of

tw

o si

des

of a

not

her

tri

angl

e.n

eith

er2.

Iden

tify

eac

h of

the

fol

low

ing

as a

n ex

ampl

e of

a r

efle

xive

,sym

met

ric,

or t

rans

itiv

epr

oper

ty.

a.If

�R

ST

��

UV

W,t

hen

�U

VW

��

RS

T.

sym

met

ric

b.

If �

RS

T�

�U

VW

and

�U

VW

��

OP

Q,t

hen

�R

ST

��

OP

Q.

tran

siti

vec.

�R

ST

��

RS

Tre

flex

ive

Rem

emb

er W

hat

Yo

u L

earn

ed3.

A g

ood

way

to

rem

embe

r so

met

hin

g is

to

expl

ain

it

to s

omeo

ne

else

.Su

ppos

e on

e of

you

rcl

assm

ates

is

hav

ing

trou

ble

un

ders

tan

din

g th

e di

ffer

ence

bet

wee

n S

AS

for

con

gru

ent

tria

ngl

es a

nd

SA

S f

or s

imil

ar t

rian

gles

.How

can

you

exp

lain

th

e di

ffer

ence

to

him

?S

amp

le a

nsw

er:

In S

AS

fo

r co

ng

ruen

ce,c

orr

esp

on

din

g s

ides

are

con

gru

ent,

wh

ile in

SA

S f

or

sim

ilari

ty,c

orr

esp

on

din

g s

ides

are

pro

po

rtio

nal

.(In

bo

th,t

he

incl

ud

ed a

ng

les

are

con

gru

ent.

)



Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

Cha

pter

723

Gle

ncoe

Geo

met

ry


Skill

s Pr

acti

ceS

imila

r Tri

ang

les

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-3

Det

erm

ine

wh

eth

er e

ach

pai

r of

tri

angl

es i

s si

mil

ar.J

ust

ify

you

r an

swer

.

1.2.

No

;th

e si

des

are

no

t p

rop

ort

ion

al.

yes;

�A

BC

��

PQ

R(o

r �

QP

R);

SS

S S

imila

rity

3.4.

yes;

�S

TU

��

JPM

;ye

s;�

SK

M�

�R

TQ

;S

AS

Sim

ilari

tyA

A S

imila

rity

ALG

EBR

AId

enti

fy t

he

sim

ilar

tri

angl

es,a

nd

fin

d x

and

th

e m

easu

res

of t

he

ind

icat

ed s

ides

.

5.A �

C�an

d E�

D�6.

J�L�an

d L�

M�

�A

BC

��

DB

E;

15;

16;

20�

JKL

��

MN

L;

10;

28;

7

7.E�

H�an

d E�

F�8.

V�T�

and

S�T�

�D

EF

��

GE

H;

4;9;

18�

RS

T�

�U

VT

;7.

5;1.

5;5

6

14

S

U

V

RT

x �

4 x �

612

9

6

9

D

E

FH G

x �

5

16

4MN

L

J

K

x �

18

x �

3

1512

D

EC

BAx

� 1

x �

5

30�

60�

RQM

S

K

T

2170

�

15

MJ

P

1470

�10

U

S

T

12

128

9

96

CP

QR

A

B

2014

1312

219 S

WX

Y

R

T

Lesson 7-3

Cha

pter

722

Gle

ncoe

Geo

met

ry

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nued

)

Sim

ilar T

rian

gle

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-3


Use

Sim

ilar

Tria

ng

les

Sim

ilar

tri

angl

es c

an b

e u

sed

to f

ind

mea

sure

men

ts.

�A

BC

��

DE

F.

Fin

d x

and

y.

� DAC F�

��B E

C F�� DA

B E��

�B EC F�

��1 98 �

� 1y 8��

�1 98 �

18x

�9(

18�

3�)9y

�32

4x

�9 �

3�y

�36

18�

3��

x

18�

�3

B CA

1818

9y

x

E FD

A p

erso

n 6

fee

t ta

ll c

asts

a 1.

5-fo

ot-l

ong

shad

ow a

t th

e sa

me

tim

eth

at a

fla

gpol

e ca

sts

a 7-

foot

-lon

gsh

adow

.How

tal

l is

th

e fl

agp

ole?

Th

e su

n’s

ray

s fo

rm s

imil

ar t

rian

gles

.U

sin

g x

for

the

hei

ght

of t

he

pole

,�6 x�

��1 7.5 �

,so

1.5

x�

42 a

nd

x�

28.

Th

e fl

agpo

le i

s 28

fee

t ta

ll.

7 ft

6 ft

?

1.5

ft

Eac

h p

air

of t

rian

gles

is

sim

ilar

.Fin

d x

and

y.

1.2.

x�

26;

y�

17.5

x�

24;

y�

30

3.4.

x�

12;

y�

24�

2�x

�19

.3;

y�

46

5.6.

x�

18;

y�

10.8

x�

10�2 3� ;

y�

16�1 2�

7.T

he

hei

ghts

of

two

vert

ical

pos

ts a

re 2

met

ers

and

0.45

met

er.W

hen

th

e sh

orte

r po

stca

sts

a sh

adow

th

at i

s 0.

85 m

eter

lon

g,w

hat

is

the

len

gth

of

the

lon

ger

post

’s s

had

ow

to t

he

nea

rest

hu

ndr

edth

?3.

78 m

y

x32

10

2230

yx

9

87.2

16

yx

6038

.623

3024

36�

�2y

x

3636

20 13

26y

x �

235

13

1020

y

x

Exam

ple

1Ex

amp

le 2

Exer

cise

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.

An

swer

s

Cha

pter

725

Gle

ncoe

Geo

met

ry


Wor

d Pr

oble

m P

ract

ice

Sim

ilar T

rian

gle

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-3

Lesson 7-3

1.M

INIA

TUR

ESM

arla

lik

es h

er c

hai

r so

mu

ch t

hat

sh

e de

cide

s to

mak

e a

min

iatu

re r

epli

ca o

f it

for

her

pet

ham

ster

.Fin

d th

e va

lue

of x

.

3.75

in.

2.M

OD

ELS

Jim

has

a s

cale

mod

el o

f h

issa

ilbo

at.T

he

figu

re s

how

s dr

awin

gs o

fth

e or

igin

al s

ailb

oat

and

the

mod

el.

Fin

d x.

160

in.

3.G

EOM

ETRY

Geo

rgia

dra

ws

a re

gula

rpe

nta

gon

an

d st

arts

con

nec

tin

g it

sve

rtic

es t

o m

ake

a 5-

poin

ted

star

.Aft

erdr

awin

g th

ree

of t

he

lin

es i

n t

he

star

,sh

ebe

com

es c

uri

ous

abou

t tw

o tr

ian

gles

that

app

ear

in t

he

figu

re,�

AB

Can

d�

BC

E.T

hey

loo

k si

mil

ar t

o h

er.P

rove

that

th

is i

s th

e ca

se.

Sam

ple

an

swer

:m

�A

DB

�10

8,so

m�

DB

A�

36 (

bas

e o

f is

o-

scel

es �

AB

D).

Th

us,

m�

AB

C�

72°.

Sim

ilarl

y,m

�D

CB

�36

°an

dm

�A

CB

�72

°.S

o,m

�B

EC

�72

°an

d m

�B

AC

�36

°.T

her

efo

re,

�A

BC

and

�B

CE

are

sim

ilar.

4.SH

AD

OW

SA

rad

io t

ower

cas

ts a

shad

ow 8

fee

t lo

ng

at t

he

sam

e ti

me

that

a v

erti

cal

yard

stic

k ca

sts

a sh

adow

hal

f an

in

ch l

ong.

How

tal

l is

th

e ra

dio

tow

er?

576

ft

MO

UN

TAIN

PEA

KS

For

Exe

rcis

es 5

an

d6,

use

th

e fo

llow

ing

info

rmat

ion

.G

avin

an

d B

rian

na

wan

t to

kn

ow h

ow f

ar a

mou

nta

in p

eak

is f

rom

th

eir

hou

ses.

Th

eym

easu

re t

he

angl

es b

etw

een

th

e li

ne

of s

ite

to t

he

peak

an

d to

eac

h o

ther

’s h

ouse

s an

dca

refu

lly

mak

e th

e dr

awin

g sh

own

.

Th

e ac

tual

dis

tan

ce b

etw

een

Gav

in a

nd

Bri

ann

a’s

hou

se i

s 1�

1 2�m

iles

.

5.W

hat

is

the

actu

al d

ista

nce

of

the

mou

nta

in p

eak

from

Gav

in’s

hou

se?

Rou

nd

you

r an

swer

to

the

nea

rest

te

nth

of

a m

ile.

12.2

mi

6.W

hat

is

the

actu

al d

ista

nce

of

the

mou

nta

in p

eak

from

Bri

ann

a’s

hou

se?

Rou

nd

you

r an

swer

to

the

nea

rest

te

nth

of

a m

ile.

12.3

mi

Gavi

n

Bria

nna

Peak

2 in

.

2.01

5 in

.0.

246

in.

90˚

83˚

A

B

D

E

C

52˚

203

in.

10.1

5 in

.8

in.

52˚

x in

.

14”

3.5

”

15”

x

Cha

pter

724

Gle

ncoe

Geo

met

ry

Prac

tice

Sim

ilar T

rian

gle

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-3


Det

erm

ine

wh

eth

er e

ach

pai

r of

tri

angl

es i

s si

mil

ar.J

ust

ify

you

r an

swer

.

1.2.

yes;

�JA

K�

�W

SY

;N

o;

the

sid

es a

re n

ot

pro

po

rtio

nal

.S

AS

Sim

ilari

ty

ALG

EBR

AId

enti

fy t

he

sim

ilar

tri

angl

es,a

nd

fin

d x

and

th

e m

easu

res

of t

he

ind

icat

ed s

ides

.

3.L �

M�an

d Q�

P�4.

N�L�

and

M�L�

�L

MN

��

PQ

N;

9;12

;8

�JL

N�

�K

LM

;2;

21;

14

Use

th

e gi

ven

in

form

atio

n t

o fi

nd

eac

h m

easu

re.

5.If

T�S�

|| Q�R�

,TS

�6,

PS

�x

�7,

6.If

E�F�

|| H�I�,

EF

�3,

EG

�x

�1,

QR

�8,

and

SR

�x

�1,

HI

�4,

and

HG

�x

�3,

fin

d P

San

d P

R.

fin

d E

Gan

d H

G.

PS

�12

;P

R�

16E

G�

6;H

G�

8

IND

IREC

T M

EASU

REM

ENT

For

Exe

rcis

es 7

an

d 8

,use

th

e fo

llow

ing

info

rmat

ion

.A

lig

hth

ouse

cas

ts a

128

-foo

t sh

adow

.A n

earb

y la

mpp

ost

that

mea

sure

s 5

feet

3 i

nch

es c

asts

an 8

-foo

t sh

adow

.

7.W

rite

a p

ropo

rtio

n t

hat

can

be

use

d to

det

erm

ine

the

hei

ght

of t

he

ligh

thou

se.

Sam

ple

an

swer

:If

x�

hei

gh

t o

f lig

hth

ou

se,�

5.x 25�

��12 88 �

.

8.W

hat

is

the

hei

ght

of t

he

ligh

thou

se?

84 f

t

F

GE

H

I

SR

P

QT

8N

JL

K

Mx

� 5

6x �

2

24

12

18N

P

QL

M

x �

3x

� 1

18

1612

.516

14

11

M

LN

SR

T42

�

42�

24

1812

16J

AK

YS

W



Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

Cha

pter

727

Gle

ncoe

Geo

met

ry


Less

on R

eadi

ng G

uide

Par

alle

l Lin

es a

nd

Pro

po

rtio

nal

Par

ts

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-4

Get

Rea

dy

for

the

Less

on

Rea

d t

he

intr

odu

ctio

n t

o L

esso

n 7

-4 i

n y

our

text

boo

k.

Use

a g

eom

etri

c id

ea t

o ex

plai

n w

hy

the

dist

ance

bet

wee

n C

hic

ago

Ave

nu

e an

dO

nta

rio

Str

eet

is s

hor

ter

alon

g M

ich

igan

Ave

nu

e th

an a

lon

g L

ake

Sh

ore

Dri

ve.

Sam

ple

an

swer

:Th

e sh

ort

est

dis

tan

ce b

etw

een

tw

o p

aral

lel l

ines

isth

e p

erp

end

icu

lar

dis

tan

ce.

Rea

d t

he

Less

on

1.P

rovi

de t

he

mis

sin

g w

ords

to

com

plet

e th

e st

atem

ent

of e

ach

th

eore

m.T

hen

sta

te t

he

nam

e of

th

e th

eore

m.

a.If

a l

ine

inte

rsec

ts t

wo

side

s of

a t

rian

gle

and

sepa

rate

s th

e si

des

into

cor

resp

ondi

ng

segm

ents

of

len

gth

s,th

en t

he

lin

e is

to

th

e

thir

d si

de.

Co

nver

se o

f th

e Tr

ian

gle

Pro

po

rtio

nal

ity

Th

eore

mb

.A

mid

segm

ent

of a

tri

angl

e is

to

on

e si

de o

f th

e tr

ian

gle

and

its

leng

th is

th

e le

ngth

of

that

sid

e.Tr

ian

gle

Mid

seg

men

t Th

eore

mc.

If a

line

is

to o

ne s

ide

of a

tri

angl

e an

d in

ters

ects

the

oth

er t

wo

side

s

in

dist

inct

poi

nts

,th

en i

t se

para

tes

thes

e si

des

into

of p

ropo

rtio

nal

len

gth

.Tr

ian

gle

Pro

po

rtio

nal

ity

Th

eore

m

2.R

efer

to

the

figu

re a

t th

e ri

ght.

a.N

ame

the

thre

e m

idse

gmen

ts o

f �

RS

T.

U�V�

,V�W�

,U�W�

b.

If R

S�

8,R

U�

3,an

d T

W�

5,fi

nd

the

len

gth

of

each

of

the

mid

segm

ents

.U

V�

5,V

W�

3,U

W�

4c.

Wh

at i

s th

e pe

rim

eter

of

�R

ST

?24

d.

Wh

at i

s th

e pe

rim

eter

of

�U

VW

?12

e.W

hat

are

th

e pe

rim

eter

s of

�R

UV

,�S

VW

,an

d �

TU

W?

12;

12;

12f.

How

are

th

e pe

rim

eter

s of

eac

h o

f th

e fo

ur

smal

l tr

ian

gles

rel

ated

to

the

peri

met

er o

fth

e la

rge

tria

ngl

e?T

he

per

imet

er o

f ea

ch s

mal

l tri

ang

le is

on

e-h

alf

the

per

imet

er o

f th

e la

rge

tria

ng

le.

g.W

ould

th

e re

lati

onsh

ip t

hat

you

fou

nd

in p

art

f ap

ply

to a

ny

tria

ngl

e in

wh

ich

th

em

idpo

ints

of

the

thre

e si

des

are

con

nec

ted?

yes

Rem

emb

er W

hat

Yo

u L

earn

ed

3.A

goo

d w

ay t

o re

mem

ber

a n

ew m

ath

emat

ical

ter

m i

s to

rel

ate

it t

o ot

her

mat

hem

atic

alvo

cabu

lary

th

at y

ou a

lrea

dy k

now

.Wh

at i

s an

eas

y w

ay t

o re

mem

ber

the

defi

nit

ion

of

mid

segm

ent

usi

ng

oth

er g

eom

etri

c te

rms?

Sam

ple

an

swer

:A

mid

seg

men

tis

ase

gm

ent

that

co

nn

ects

th

e m

idp

oin

tso

f tw

o s

ides

of

a tr

ian

gle

.

R U

V W

T

S

seg

men

tstw

op

aral

lel

on

e-h

alf

par

alle

l

par

alle

lp

rop

ort

ion

al

Lesson 7-4

Cha

pter

726

Gle

ncoe

Geo

met

ry

Enri

chm

ent

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-3

Mov

ing

Sh

adow

sH

ave

you

eve

r w

atch

ed y

our

shad

ow a

s yo

u

wal

ked

alon

g th

e st

reet

at

nig

ht

and

obse

rved

how

its

sh

ape

chan

ges

as y

ou m

ove?

Su

ppos

ea

man

wh

o is

6 f

eet

tall

is

stan

din

g be

low

a

lam

ppos

t th

at i

s 20

fee

t ta

ll.T

he

man

is

wal

kin

g aw

ay f

rom

th

e la

mpp

ost

at a

rat

e of

5

feet

per

sec

ond.

1.If

th

e m

an i

s m

ovin

g at

a r

ate

of 5

fee

t pe

rse

con

d,m

ake

a co

nje

ctu

re a

s to

th

e ra

teth

at h

is s

had

ow i

s m

ovin

g.S

amp

le a

nsw

er:

His

sh

ado

w is

mov

ing

mo

re q

uic

kly

than

he

is.

2.H

ow f

ar a

way

fro

m t

he

lam

ppos

t is

th

e m

an a

fter

8 s

econ

ds?

40 f

t

3.H

ow f

ar i

s th

e en

d of

his

sh

adow

fro

m t

he

bott

om o

f th

e la

mpp

ost

afte

r 8

seco

nds

? U

se s

imil

ar t

rian

gles

to

solv

e th

is p

robl

em.

57.1

4 ft

4.A

fter

3 m

ore

seco

nds

,how

far

fro

m t

he

lam

ppos

t is

th

e m

an?

How

far

fro

m t

he

lam

ppos

t is

his

sh

adow

?55

fee

t;78

.57

ft

5.H

ow m

any

feet

did

th

e m

an m

ove

in 3

sec

onds

? H

ow m

any

feet

did

th

e sh

adow

mov

e in

3 s

econ

ds?

15 f

eet;

21.4

3 ft

6.T

he

man

is

mov

ing

at a

rat

e of

5 f

eet/

seco

nd.

Wh

at r

ate

is h

is s

had

ow m

ovin

g?H

ow d

oes

this

rat

e co

mpa

re t

o th

e co

nje

ctu

re y

ou m

ade

in p

robl

em 1

? M

ake

aco

nje

ctu

re a

s to

wh

y th

e re

sult

s ar

e li

ke t

his

.7.

14 f

t/s;

Sam

ple

an

swer

:H

is s

had

ow

is g

etti

ng

lon

ger

as

he

mov

es f

urt

her

aw

ay f

rom

th

e la

mp

po

st.

20

ft

6 ft

x ft

5 ft

/sec


Answers (Lessons 7–3 and 7–4)


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

An

swer

s

Cha

pter

729

Gle

ncoe

Geo

met

ry


Stud

y G

uide

and

Inte

rven

tion

(co

nti

nued

)

Par

alle

l Lin

es a

nd

Pro

po

rtio

nal

Par

ts

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-4

Div

ide

Seg

men

ts P

rop

ort

ion

ally

Wh

en

thre

e or

mor

e pa

rall

el l

ines

cu

t tw

o tr

ansv

ersa

ls,

they

sep

arat

e th

e tr

ansv

ersa

ls i

nto

pro

port

ion

al

part

s.If

th

e ra

tio

of t

he

part

s is

1,t

hen

th

e pa

rall

elli

nes

sep

arat

e th

e tr

ansv

ersa

ls i

nto

con

gru

ent

part

s.

If �

1|| �

2|| �

3,If

�4

|| �5

|| �6

and

then

�a b��

� dc � .�u v�

�1,

then

�w x��

1.

Ref

er t

o li

nes

�1,

� 2,a

nd

�3

abov

e.If

a�

3,b

�8,

and

c�

5,fi

nd

d.

� 1|| �

2|| �

3so

�3 8��

� d5 � .T

hen

3d

�40

an

d d

�13

�1 3� .

Fin

d x

and

y.

1.2.

x�

8x

�9

3.4.

x�

5;y

�2

y�

3�1 3�

5.6.

x�

12y

�3

1632

y �

3y

34

x �

4x

5

8y

� 2

y2x

� 4

3 x �

12y

� 2

3 y

2x �

6

x �

3

12

x �

12

123x5x

a

bd

uv

xw

ct

n m

s� 1

� 4� 5

� 6

� 2

� 3

Exam

ple

Exer

cise

s

Lesson 7-4

Cha

pter

728

Gle

ncoe

Geo

met

ry

Stud

y G

uide

and

Inte

rven

tion

Par

alle

l Lin

es a

nd

Pro

po

rtio

nal

Par

ts

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-4


Pro

po

rtio

nal

Par

ts o

f Tr

ian

gle

sIn

an

y tr

ian

gle,

a li

ne

para

llel

to

one

side

of

a tr

ian

gle

sepa

rate

s th

e ot

her

tw

o si

des

prop

orti

onal

ly.T

he

con

vers

e is

als

o tr

ue.

If X

and

Yar

e th

e m

idpo

ints

of

R �T�

and

S�T�

,th

en X�

Y�is

am

idse

gmen

tof

th

e tr

ian

gle.

Th

e T

rian

gle

Mid

segm

ent

Th

eore

mst

ates

th

at a

mid

segm

ent

is p

aral

lel

to t

he

thir

d si

de a

nd

is h

alf

its

len

gth

.

If X

Y� �

�|| R

S��

� ,th

en �R X

TX ��

� YSY T�

.

If �R X

TX ��

� YSY T�

,th

en X

Y��

�|| R

S��

� .

If X �

Y�is

a m

idse

gmen

t,th

en X

Y��

�|| R

S��

�an

d X

Y�

�1 2� RS

.

YS

T

R

X

In �

AB

C,E�

F�|| C�

B�.F

ind

x.

Sin

ce E�

F�|| C�

B�,�

FABF �

�� EA

E C�.

�x x� �2 22

��

�1 68 �

6x�

132

�18

x�

3696

�12

x8

�x

F

C

BA

18

x �

22

x �

2

6E

A t

rian

gle

has

ver

tice

sD

(3,6

),E

(�3,

�2)

,an

d F

(7,�

2).

Mid

segm

ent

G �H�

is p

aral

lel

to E�

F�.F

ind

th

e le

ngt

h o

f G �

H�.

G �H�

is a

mid

segm

ent,

so i

ts l

engt

h i

s on

e-h

alf

that

of

E �F�

.Poi

nts

Ean

d F

hav

e th

esa

me

y-co

ordi

nat

e,so

EF

�7

�(�

3) �

10.

Th

e le

ngt

h o

f m

idse

gmen

t G �

H�is

5.

Fin

d x

.

1.7

2.10

3.17

.5

4.8

5.12

6.5

7.In

Exa

mpl

e 2,

fin

d th

e sl

ope

of E�

F�an

d sh

ow t

hat

E�F�

|| G�H�

.

Th

e en

dp

oin

ts o

f G�

H�ar

e at

(0,

2) a

nd

(5,

2).T

he

slo

pe

of

G�H�

is 0

an

d t

he

slo

pe

of

E �F�

is 0

.G�H�

and

E�F�

are

par

alle

l.

3010

x �

10

x11

x �

12

x33

3010

24x

35x9

20

x

185

5x

7

Exam

ple

1Ex

amp

le 2

Exer

cise

s



Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

Cha

pter

731

Gle

ncoe

Geo

met

ry


Prac

tice

Par

alle

l Lin

es a

nd

Pro

po

rtio

nal

Par

ts

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-4

1.If

AD

�24

,DB

�27

,an

d E

B�

18,

2.F

ind

x,Q

T,a

nd

TR

if Q

T�

x�

6,fi

nd

CE

.S

R�

12,P

S�

27,a

nd

TR

�x

�4.

1612

;18

;8

Det

erm

ine

wh

eth

er J�

K�|| N�

M�.

3.J

N�

18,J

L�

30,K

M�

21,a

nd

ML

�35

no

4.K

M�

24,K

L�

44,a

nd

NL

��5 6� J

N

yes

CO

OR

DIN

ATE

GEO

MET

RYF

or E

xerc

ises

5 a

nd

6,u

se t

he

foll

owin

g in

form

atio

n.

Tri

angl

e E

FG

has

ver

tice

s E

(�4,

�1)

,F(2

,5),

and

G(2

,�1)

.Poi

nt

Kis

th

e m

idpo

int

of E �

G�an

d H

is t

he

mid

poin

t of

F�G�

.

5.S

how

th

at E�

F�is

par

alle

l to

K�H�

.

Th

e sl

op

e o

f E�

F�is

1 a

nd

th

e sl

op

e o

f K�

H�is

1,

so E�

F�is

par

alle

l to

K�H�

.

6.S

how

th

at K

H�

�1 2� EF

.

Th

e le

ng

th o

f K�

H�is

3�

2�,an

d t

he

len

gth

of

E�F�

is 6

�2�.

7.F

ind

xan

d y.

8.F

ind

xan

d y.

x�

4,y

�9

x�

�5 2� ,y

��9 4�

9.M

APS

Th

e di

stan

ce f

rom

Wil

min

gton

to

Ash

Gro

ve a

lon

g K

enda

ll i

s 82

0 fe

et a

nd

alon

g M

agn

olia

,660

fee

t.If

th

e di

stan

ce b

etw

een

Bee

ch a

nd

Ash

Gro

ve a

lon

g M

agn

olia

is

280

feet

,wh

at i

s th

e di

stan

ce b

etw

een

th

e tw

o st

reet

s al

ong

Ken

dall

?

abo

ut

348

ft

Ash

Grov

e

Beec

h

Mag

nolia

Kend

all

Wilm

ingt

on

4 – 3y �

2

3 x �

4x

� 1

4 y �

43x

� 4

2 – 3y �

31 – 3y

� 6

5 – 4x �

3

x

y

O

EGF H

K

NL

J

KM

S

Q

TR

P

D

EC BA

Lesson 7-4

Cha

pter

730

Gle

ncoe

Geo

met

ry

Skill

s Pr

acti

ceP

aral

lel L

ines

an

d P

rop

ort

ion

al P

arts

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-4


1.If

JK

�7,

KH

�21

,an

d J

L�

6,2.

Fin

d x

and

TV

if R

U�

8,U

S�

14,

fin

d L

I.T

V�

x�

1 an

d V

S�

17.5

.

1811

;10

Det

erm

ine

wh

eth

er B�

C�|| D�

E�.

3.A

D�

15,D

B�

12,A

E�

10,a

nd

EC

�8

yes

4.B

D�

9,B

A�

27,a

nd

CE

is o

ne

thir

d of

EA

no

5.A

E�

30,A

C�

45,a

nd

AD

is t

wic

e D

B

yes

CO

OR

DIN

ATE

GEO

MET

RYF

or E

xerc

ises

6–8

,use

th

e fo

llow

ing

info

rmat

ion

.T

rian

gle

AB

Ch

as v

erti

ces

A(�

5,2)

,B(1

,8),

and

C(4

,2).

Poi

nt

Dis

th

e m

idpo

int

of A �

B�an

d E

is t

he

mid

poin

t of

A�C�

.

6.Id

enti

fy t

he

coor

din

ates

of

Dan

d E

.

D(�

2,5)

;E

(�0.

5,2)

7.S

how

th

at B�

C�is

par

alle

l to

D�E�

.

Sin

ce t

he

slo

pe

of

B�C�

is �

2 an

d t

he

slo

pe

of

D�E�

is �

2,B�

C�is

par

alle

l to

D�E�.

8.S

how

th

at D

E�

�1 2� BC

.

Th

e le

ng

th o

f D�

E�is

�11

.25

�o

r o

r �3 �

25�

� a

nd

th

e le

ng

th o

f B�

C�is

�45�

or

3 �5 �.

9.F

ind

xan

d y.

10.F

ind

xan

d y.

x�

6,y

�6.

5x

�2,

y�

4

3 – 2x �

2

x �

3

2 y �

1

3y �

52x

� 1

3y �

8y

� 5

x �

7

�45�

�2

x

y

O

AC

B

D

E

CB

ED

A

R

UV

T

S

HL

KJ

I



Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

An

swer

s

Cha

pter

733

Gle

ncoe

Geo

met

ry


Enri

chm

ent

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-4

Par

alle

l Lin

es a

nd

Co

ng

ruen

t P

arts

Th

ere

is a

th

eore

m s

tati

ng

that

if

thre

e pa

rall

el l

ines

cu

t of

f co

ngr

uen

t se

gmen

ts o

n o

ne

tran

sver

sal,

then

th

ey c

ut

off

con

gru

ent

segm

ents

on

an

y tr

ansv

ersa

l.T

his

can

be

show

n f

oran

y n

um

ber

of p

aral

lel

lin

es.T

he

foll

owin

g dr

afti

ng

tech

niq

ue

use

s th

is f

act

to d

ivid

e a

segm

ent

into

con

gru

ent

part

s.

A �B�

is t

o be

sep

arat

ed i

nto

fiv

e co

ngr

uen

t pa

rts.

Th

is c

an b

e do

ne

very

acc

ura

tely

wit

hou

t u

sin

g a

rule

r.A

ll t

hat

is

nee

ded

is a

com

pass

an

d a

piec

e of

not

eboo

k pa

per.

Ste

p 1

Hol

d th

e co

rner

of

a pi

ece

of n

oteb

ook

pape

r at

po

int

A.

Ste

p 2

Fro

m p

oin

t A

,dra

w a

seg

men

t al

ong

the

pape

r th

at i

s fi

ve s

pace

s lo

ng.

Mar

k w

her

e th

e li

nes

of

th

e n

oteb

ook

pape

r m

eet

the

segm

ent.

Lab

el

the

fift

h p

oin

t,P.

Ste

p 3

Dra

w P�

B�.T

hro

ugh

eac

h o

f th

e ot

her

mar

ks

on A �

P�,c

onst

ruct

a l

ine

para

llel

to

B�P�

.Th

e po

ints

wh

ere

thes

e li

nes

in

ters

ect

A �B�

wil

l di

vide

A �B�

into

fiv

e co

ngr

uen

t se

gmen

ts.

Use

a c

omp

ass

and

a p

iece

of

not

eboo

k p

aper

to

div

ide

each

seg

men

t in

to t

he

give

n n

um

ber

of

con

gru

ent

par

ts.

See

stu

den

t’s w

ork

.

1.si

x co

ngr

uen

t pa

rts

2.se

ven

con

gru

ent

part

sA

B

AB

A

P

B

AB

P

AB

AB

Lesson 7-4

Cha

pter

732

Gle

ncoe

Geo

met

ry

Wor

d Pr

oble

m P

ract

ice

Par

alle

l Lin

es a

nd

Pro

po

rtio

nal

Par

ts

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-4


1.C

AR

PEN

TRY

Jake

is

fixi

ng

an A

-fra

me.

He

wan

ts t

o ad

d a

hor

izon

tal

supp

ort

beam

hal

fway

up

and

para

llel

to

the

grou

nd.

How

lon

g sh

ould

th

isbe

am b

e?4

ft

2.ST

REE

TSIn

th

e di

agra

m,C

ay S

tree

tan

d B

ay S

tree

t ar

e pa

rall

el.F

ind

x.

1.12

km

3.JU

NG

LE G

YM

SP

rass

ad i

s bu

ildi

ng

atw

o-st

ory

jun

gle

gym

acc

ordi

ng

to t

he

plan

s sh

own

.Fin

d x.

13 f

t 4

in.

4.FI

REM

ENA

cat

is

stu

ck i

n a

tre

ean

d fi

rem

en t

ry t

ore

scu

e it

.Bas

edon

th

e fi

gure

,if

afi

rem

an c

lim

bs

to t

he

top

of t

he

ladd

er,h

ow f

araw

ay i

s th

e ca

t?34

.5 f

t

EQU

AL

PAR

TSF

or E

xerc

ises

5 a

nd

6,

use

th

e fo

llow

ing

info

rmat

ion

.N

ick

has

a s

tick

th

at h

e w

ould

lik

e to

di

vide

in

to 9

equ

al p

arts

.He

plac

es i

t on

a p

iece

of

grid

pap

er a

s sh

own

.Th

e gr

id p

aper

is

rule

d so

th

at v

erti

cal

and

hor

izon

tal

lin

es a

re e

qual

ly s

pace

d.

5.E

xpla

in h

ow h

e ca

n u

se t

he

grid

pap

erto

hel

p h

im f

ind

wh

ere

he

nee

ds t

o cu

tth

e st

ick.

Bec

ause

he

po

siti

on

ed t

he

stic

kso

th

at it

s en

ds

are

tou

chin

gh

ori

zon

tal l

ines

th

at a

re 9

un

its

apar

t,h

e ca

n c

ut

the

stic

kw

her

ever

oth

er h

ori

zon

tal l

ines

inte

rsec

t it

.

6.S

upp

ose

Nic

k w

ants

to

divi

de h

is s

tick

into

5 e

qual

par

ts u

tili

zin

g th

e gr

idpa

per.

Wh

at c

an h

e do

?H

e ca

n r

ota

te t

he

stic

k so

itto

uch

es h

ori

zon

tal l

ines

5 u

nit

sap

art

and

ap

ply

th

e sa

me

met

ho

d.

Mee

eeow

ww

!

30 ft

.

40 ft

.46

ft.x

8 ft.

8 ft.

10 ft

.

24 ft.

10 ft

.x

Cay

St.

1 km

1.4

km

0.8

km

Bay

St.

Dale St.

Earl St.

(not

dra

wn

to s

cale

)

x

8 fe

et



Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

Cha

pter

735

Gle

ncoe

Geo

met

ry


Stud

y G

uide

and

Inte

rven

tion

Par

ts o

f S

imila

r Tri

ang

les

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-5

Peri

met

ers

If t

wo

tria

ngl

es a

re s

imil

ar,t

hei

r pe

rim

eter

s h

ave

the

sam

e pr

opor

tion

as

the

corr

espo

ndi

ng

side

s.

If �

AB

C�

�R

ST

,th

en

�A RB S

� �B S

TC��

RATC

��

�A RB S�

��B S

TC ��

� RAC T�

.

Use

th

e d

iagr

am a

bov

e w

ith

�A

BC

��

RS

T.I

f A

B�

24 a

nd

RS

�15

,fi

nd

th

e ra

tio

of t

hei

r p

erim

eter

s.S

ince

�A

BC

��

RS

T,t

he

rati

o of

th

e pe

rim

eter

s of

�A

BC

and

�R

ST

is t

he

sam

e as

th

era

tio

of c

orre

spon

din

g si

des.

Th

eref

ore

��2 14 5�

��8 5�

Eac

h p

air

of t

rian

gles

is

sim

ilar

.Fin

d t

he

per

imet

er o

f th

e in

dic

ated

tri

angl

e.

1.�

XY

Z2.

�B

DE

3345

3.�

AB

C4.

�X

YZ

8455

.4

5.�

AB

C6.

�R

ST

5411

0

25 20

10

PT

SM

R

95

13

12

AD

E

C

B

56

8.7

13

10

XY

ZT

RS

18

202515

17 8

NB

AC

PM

36

9 11 CDE

A

B

44

24

2022

10

TR

XZ

YS

peri

met

er o

f �

AB

C�

��

peri

met

er o

f �

RS

T

AC

BS

RT

Exam

ple

Exer

cise

s

Lesson 7-5

Cha

pter

734

Gle

ncoe

Geo

met

ry

Less

on R

eadi

ng G

uide

Par

ts o

f S

imila

r Tri

ang

les

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-5


Get

Rea

dy

for

the

Less

on

Rea

d t

he

intr

odu

ctio

n t

o L

esso

n 7

-5 i

n y

our

text

boo

k.

•H

ow i

s si

mil

arit

y in

volv

ed i

n t

he

proc

ess

of m

akin

g a

phot

ogra

phic

pri

nt

from

an

egat

ive?

Sam

ple

an

swer

:Th

e p

rin

t is

an

en

larg

ed v

ersi

on

of

the

neg

ativ

e.T

he

imag

e o

n t

he

pri

nt

is s

imila

r to

th

e im

age

on

th

e n

egat

ive,

sow

hen

yo

u lo

ok

at t

he

pri

nt,

you

will

see

exa

ctly

th

e sa

me

thin

gs

inth

e sa

me

pro

po

rtio

ns

as o

n t

he

neg

ativ

e,ju

st la

rger

.•

Wh

y do

ph

otog

raph

ers

plac

e th

eir

cam

eras

on

tri

pods

?

Sam

ple

an

swer

:Th

ree

po

ints

det

erm

ine

a p

lan

e,so

th

e th

ree

feet

of

the

trip

od

are

co

pla

nar

an

d t

he

trip

od

will

no

t w

ob

ble

.

Rea

d t

he

Less

on

1.In

th

e fi

gure

,�R

ST

��

UV

W.C

ompl

ete

each

pr

opor

tion

in

volv

ing

the

len

gth

s of

seg

men

ts i

nth

is f

igu

re b

y re

plac

ing

the

ques

tion

mar

k.T

hen

iden

tify

th

e de

fin

itio

n o

r th

eore

m f

rom

th

e li

stbe

low

th

at t

he

com

plet

ed p

ropo

rtio

n i

llu

stra

tes.

i.D

efin

itio

n o

f co

ngr

uen

t po

lygo

ns

ii.

Def

init

ion

of

sim

ilar

pol

ygon

s

iii.

Pro

port

ion

al P

erim

eter

s T

heo

rem

iv.

An

gle

Bis

ecto

rs T

heo

rem

v.S

imil

ar t

rian

gles

hav

e co

rres

pon

din

g al

titu

des

prop

orti

onal

to

corr

espo

ndi

ng

side

s.

vi.

Sim

ilar

tri

angl

es h

ave

corr

espo

ndi

ng

med

ian

s pr

opor

tion

al t

o co

rres

pon

din

g si

des.

vii.

Sim

ilar

tria

ngle

s ha

ve c

orre

spon

ding

ang

le b

isec

tors

pro

port

iona

l to

corr

espo

ndin

g si

des.

a.�R

S�

S ?T�

TR

��

� URS V�

UV

�V

W�

WU

;iii

b.

� URWT �

��S ?X �

VY

;v

c.�R U

M N��

� V? W�S

T;

vid

.� UR

S V��

�S ?T �V

W;

ii

e.�R P

SP ��

� S? T�R

T;

ivf.

�U ?N ��

�U RW T�

RM

;vi

g.� WT

P Q��

�R ?T �U

W;

vii

h.

�U VWW �

�� Q? V�

UQ

;iv

Rem

emb

er W

hat

Yo

u L

earn

ed

2.A

goo

d w

ay t

o re

mem

ber

a la

rge

amou

nt

of i

nfo

rmat

ion

is

to r

emem

ber

key

wor

ds.W

hat

key

wor

ds w

ill

hel

p yo

u r

emem

ber

the

feat

ure

s of

sim

ilar

tri

angl

es t

hat

are

pro

port

ion

alto

th

e le

ngt

hs

of t

he

corr

espo

ndi

ng

side

s?

per

imet

ers,

alti

tud

es,a

ng

le b

isec

tors

,med

ian

s

W

QN

YU

V

T

PM

XR

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.

An

swer

s

Cha

pter

737

Gle

ncoe

Geo

met

ry


Skill

s Pr

acti

ceP

arts

of

Sim

ilar T

rian

gle

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-5

Fin

d t

he

per

imet

er o

f th

e gi

ven

tri

angl

e.

1.�

JK

L,i

f �

JK

L�

�R

ST

,RS

�14

,2.

�D

EF

,if

�D

EF

��

AB

C,A

B�

27,

ST

�12

,TR

�10

,an

d L

J�

14B

C�

16,C

A�

25,a

nd

FD

�15

50.4

40.8

3.�

PQ

R,i

f �

PQ

R�

�L

MN

,LM

�16

,4.

�K

LM

,if

�K

LM

��

FG

H,F

G�

30,

MN

�14

,NL

�27

,an

d R

P�

18G

H�

38,H

F�

38,a

nd

KL

�24

3884

.8

Use

th

e gi

ven

in

form

atio

n t

o fi

nd

eac

h m

easu

re.

5.F

ind

FG

if �

RS

T�

�E

FG

,S�H�

is a

n

6.F

ind

MN

if �

AB

C�

�M

NP,

A�D�

is a

n

alti

tude

of

�R

ST

,F �J�

is a

n a

ltit

ude

of

alti

tude

of

�A

BC

,M�Q�

is a

n a

ltit

ude

of

�E

FG

,ST

�6,

SH

�5,

and

FJ

�7.

�M

NP

,AB

�24

,AD

�14

,and

MQ

�10

.5.

8.4

18

Fin

d x

.

7.�

HK

L�

�X

YZ

8.

8�1 3�

8.4

LH

K

18

10

Y

15

x

ZX

7

20

24

x

C

A

BD

PN

QM

JG

E

F

HT

R

S

GL K

M

F

H

LM

PQ

RN

A

BC

D

EF

RS

T

JK

L

Lesson 7-5

Cha

pter

736

Gle

ncoe

Geo

met

ry

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nued

)

Par

ts o

f S

imila

r Tri

ang

les

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-5


Spec

ial S

egm

ents

of

Sim

ilar

Tria

ng

les

Wh

en t

wo

tria

ngl

es a

re s

imil

ar,

corr

espo

ndi

ng

alti

tude

s,an

gle

bise

ctor

s,an

d m

edia

ns

are

prop

orti

onal

to

the

corr

espo

ndi

ng

side

s.A

lso,

in a

ny

tria

ngl

e an

an

gle

bise

ctor

sep

arat

es t

he

oppo

site

sid

e in

to s

egm

ents

th

ath

ave

the

sam

e ra

tio

as t

he

oth

er t

wo

side

s of

th

e tr

ian

gle.

In t

he

figu

re,

�A

BC

��

XY

Z,w

ith

an

gle

bis

ecto

rs a

ssh

own

.Fin

d x

.

Sin

ce �

AB

C�

�X

YZ

,th

e m

easu

res

of t

he

angl

e bi

sect

ors

are

prop

orti

onal

to

the

mea

sure

s of

a p

air

of c

orre

spon

din

g si

des.

�A XB Y�

�� YB

WD �

�2 x4 ��

�1 80 �

10x

�24

(8)

10x

�19

2x

�19

.2

2410 D

W

Y

ZX

C

B

A

8x

S�U�

bis

ects

�R

ST

.Fin

d x

.

Sin

ce S �

U�is

an

an

gle

bise

ctor

,�R T

UU ��

�R TSS �

.

� 2x 0��

�1 35 0�

30x

�20

(15)

30x

�30

0x

�10

x2030

15

UT

S

R

Fin

d x

for

each

pai

r of

sim

ilar

tri

angl

es.

1.2.

108

3.4.

2.25

8.75

5.6.

12�5 6�

15

2x �

2x

� 1

2816

17

11

x �

7

x

10

10x

8

87

3

3

4x

69

12x

x

36

1820

Exam

ple

1Ex

amp

le 2

Exer

cise

s



Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.

Cha

pter

739

Gle

ncoe

Geo

met

ry


Wor

d Pr

oble

m P

ract

ice

Par

ts o

f S

imila

r Tri

ang

les

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-5

Lesson 7-5

1.JO

GG

ING

Mac

y w

ants

to

jog

arou

nd

Tri

angl

e P

ark.

On

a s

cale

map

,th

e pa

rkh

as a

per

imet

er o

f 11

in

ches

.Th

e sc

ale

of t

he

map

is

1 in

ch :

100

yard

s.W

hat

is

the

peri

met

er o

f th

e ac

tual

par

k?11

00 y

d

2.TE

NTS

Jan

a w

ent

cam

pin

g an

d st

ayed

in a

ten

t sh

aped

lik

e a

tria

ngl

e.In

aph

oto

of t

he

ten

t,th

e ba

se o

f th

e te

nt

is6

inch

es a

nd

the

alti

tude

is

5 in

ches

.Th

eac

tual

bas

e w

as 1

2 fe

et l

ong.

Wh

at w

asth

e h

eigh

t of

th

e ac

tual

ten

t?

10 f

t

3.PL

AY

GR

OU

ND

Th

e pl

aygr

oun

d at

Han

k’s

sch

ool

has

a l

arge

rig

ht

tria

ngl

epa

inte

d in

th

e gr

oun

d.H

ank

star

ts

at t

he

righ

t an

gle

corn

er a

nd

wal

ksto

war

d th

e op

posi

te s

ide

alon

g an

an

gle

bise

ctor

an

d st

ops

wh

en h

e ge

ts t

o th

eh

ypot

enu

se.

How

mu

ch f

arth

er f

rom

Han

k is

poi

nt

Bve

rsu

s po

int

A?

7�1 7�

ft

4.FL

AG

PO

LES

A f

lag

pole

att

ach

ed t

oth

e si

de o

f a

buil

din

g is

su

ppor

ted

wit

h

a n

etw

ork

of s

trin

gs a

s sh

own

in

th

efi

gure

.

Th

e ri

ggin

g is

don

e so

th

at A

E�

EF

,A

C�

CD

,an

d A

B�

BC

.Wh

at i

s th

era

tio

of C

Fto

BE

?2

:1

CO

PIES

For

Exe

rcis

es 5

an

d 6

,use

th

efo

llow

ing

info

rmat

ion

.G

ordo

n m

ade

a ph

otoc

opy

of a

pag

e fr

om

his

geo

met

ry b

ook

to e

nla

rge

one

of t

he

figu

res.

Th

e ac

tual

fig

ure

th

at h

e co

pied

is

show

n b

elow

.

Th

e ph

otoc

opy

cam

e ou

t po

orly

.Gor

don

cou

ld n

ot r

ead

the

nu

mbe

rs o

n t

he

phot

ocop

y,al

thou

gh t

he

tria

ngl

e it

self

w

as c

lear

.Gor

don

mea

sure

d th

e ba

se o

f th

e en

larg

ed t

rian

gle

and

fou

nd

it t

o be

20

0 m

illi

met

ers.

5.W

hat

is

the

len

gth

of

the

draw

n a

ltit

ude

of t

he

enla

rged

tri

angl

e? R

oun

d yo

ur

answ

er t

o th

e n

eare

st m

illi

met

er.

149

mm

6.W

hat

is

the

len

gth

of

the

draw

n m

edia

nof

th

e en

larg

ed t

rian

gle?

Rou

nd

you

ran

swer

to

the

nea

rest

mil

lim

eter

.15

4 m

m

39 m

mMedian

Altitude

30 m

m

29 m

m

AB

C

DF E

A

B

45˚

30 ft

40 ft

50 ft

x

Cha

pter

738

Gle

ncoe

Geo

met

ry

Prac

tice

Par

ts o

f S

imila

r Tri

ang

les

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-5


Fin

d t

he

per

imet

er o

f th

e gi

ven

tri

angl

e.

1.�

DE

F,i

f �

AB

C�

�D

EF

,AB

�36

,2.

�S

TU

,if

�S

TU

��

KL

M,K

L�

12,

BC

�20

,CA

�40

,an

d D

E�

35L

M�

31,M

K�

32,a

nd

US

�28

93.3�

65.6

25

Use

th

e gi

ven

in

form

atio

n t

o fi

nd

eac

h m

easu

re.

3.F

ind

PR

if �

JK

L�

�N

PR

,K�M�

is a

n

4.F

ind

ZY

if �

ST

U�

�X

YZ

,U�A�

is a

n

alti

tude

of

�J

KL

,P �T�

is a

n a

ltit

ude

of

alti

tude

of

�S

TU

,Z�B�

is a

n a

ltit

ude

of

�N

PR

,KL

�28

,KM

�18

,an

d �

XY

Z,U

T�

8.5,

UA

�6,

and

PT

�15

.75.

ZB

�11

.4.

24.5

16.1

5

Fin

d x

.

5.6.

13.5

16.8

PHO

TOG

RA

PHY

For

Exe

rcis

es 7

an

d 8

,use

th

e fo

llow

ing

info

rmat

ion

.F

ran

cin

e h

as a

cam

era

in w

hic

h t

he

dist

ance

fro

m t

he

len

s to

th

e fi

lm i

s 24

mil

lim

eter

s.

7.If

Fra

nci

ne

take

s a

full

-len

gth

ph

otog

raph

of

her

fri

end

from

a d

ista

nce

of

3 m

eter

s an

dth

e h

eigh

t of

her

fri

end

is 1

40 c

enti

met

ers,

wh

at w

ill

be t

he

hei

ght

of t

he

imag

e on

th

efi

lm?

(Hin

t:C

onve

rt t

o th

e sa

me

un

it o

f m

easu

re.)

11.2

mm

8.S

upp

ose

the

hei

ght

of t

he

imag

e on

th

e fi

lm o

f h

er f

rien

d is

15

mil

lim

eter

s.If

Fra

nci

ne

took

a f

ull

-len

gth

sh

ot,w

hat

was

th

e di

stan

ce b

etw

een

th

e ca

mer

a an

d h

er f

rien

d?2.

24 m

x28

2030

402x

� 1

25x

� 4

YX

BZ

TS

AU

MJ

L

K

TN

R

P

KS

LT

UM

B E

CF

DA



Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

An

swer

s

Cha

pter

741

Gle

ncoe

Geo

met

ry


Spre

adsh

eet

Act

ivit

yF

ract

als

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-5

You

can

use

a s

prea

dsh

eet

to c

reat

e a

Sie

rpin

ski t

rian

gle.

Use

a s

pre

adsh

eet

to c

reat

e a

Sie

rpin

ski

tria

ngl

e.

Ste

p 1

In c

ell A

2,en

ter

1.In

cel

l A3,

ente

r an

equ

als

sign

fol

low

ed b

y A

2�1

.Th

is w

ill

retu

rn t

he

nu

mbe

r of

ite

rati

ons.

Cli

ck o

n t

he

bott

om r

igh

t co

rner

of

cell

A2

and

drag

it

thro

ugh

cel

l A50

0 to

get

500

ite

rati

ons.

Ste

p 2

In c

ell

B1,

ente

r 0.

5.T

his

in

dica

tes

the

mid

poin

ts o

f th

e se

gmen

ts.

Ste

p 3

In c

ell

C1,

ente

r 1

and

in c

ell

D1,

ente

r 0.

3.S

tep

4In

cel

l B

2,en

ter

an e

qual

s si

gn f

ollo

wed

by

3*R

AN

D()

.Cli

ck o

n t

he

bott

om r

igh

tco

rner

of

cell

B2

and

drag

in

th

rou

gh c

ell

B50

0 to

get

500

ite

rati

ons.

Ste

p 5

In c

ell

C2,

ente

r an

equ

als

sign

fol

low

ed b

y th

e re

curs

ive

form

ula

IF(B

2<1,

(1�

$B$1

)*C

1,IF

(B2�

2,(1

�$B

$1)*

C1�

$B$1

,(1�

$B$1

)*C

1�2*

$B$1

)).T

his

wil

l re

turn

th

e x

valu

es o

f th

e po

ints

to

be g

raph

ed.C

lick

on

th

e bo

ttom

rig

ht

corn

er o

f ce

ll C

2 an

d dr

ag t

hro

ugh

cel

l C

500.

Ste

p 6

In c

ell

D2,

ente

r an

equ

als

sign

fol

low

ed b

y th

e re

curs

ive

form

ula

IF(B

2�1,

(1�

$B$1

)*D

1,IF

(B2�

2,(1

�$B

$1)*

D1�

$B$1

,(1�

$B$1

)*D

1)).

Th

is w

ill

retu

rn t

he

yva

lues

of

the

poin

ts t

o be

gra

phed

.Cli

ck o

n t

he

bott

om r

igh

t co

rner

of

cell

D2

and

drag

th

rou

ghce

ll D

500.

Ste

p 7

To

grap

h t

he

valu

es i

nco

lum

ns

C a

nd

D,f

irst

h

igh

ligh

t al

l of

th

e da

ta

in t

he

two

colu

mn

s.N

ext,

choo

se t

he

char

t w

izar

dfr

om t

he

tool

bar.

Sel

ect

XY

(Sca

tter

).P

ress

Nex

t,N

ext.

Th

en s

elec

t th

e G

ridl

ines

tab

and

un

chec

k th

e M

ajor

gri

dlin

es.T

hen

pre

ss N

ext

and

Fin

ish

.T

his

wil

l re

turn

th

e S

ierp

insk

i tr

ian

gle.

An

alyz

e yo

ur

dra

win

g.1.

Wh

at h

appe

ns

to y

our

draw

ing

if y

ou h

ave

mor

e it

erat

ion

s? T

ry 1

000,

2000

,an

d 50

00.

Th

e p

ictu

re lo

oks

sh

arp

er w

ith

mo

re it

erat

ion

s.2.

Ch

ange

th

e 0.

5 to

2\3

in c

ell B

1.(H

int:

You

may

nee

d to

en

ter

0.66

6666

for

2\3

.) H

owdo

es t

his

ch

ange

th

e pi

ctu

re?

See

stu

den

ts’w

ork

.3.

Ch

ange

0.3

to

0.6

in c

ell D

1.H

ow d

oes

this

ch

ange

th

e dr

awin

g?

See

stu

den

ts’w

ork

.4.

En

ter

the

foll

owin

g in

to a

new

spr

eads

hee

t an

d de

scri

be w

hat

you

see

.S

tep

1:In

cel

l A2,

ente

r th

e fo

rmu

la �

A1.

Ste

p 2:

In c

ell B

2,en

ter

the

form

ula

� A

1�B

1.S

tep

3:C

lick

on

th

e bo

ttom

rig

ht

corn

er o

f ce

ll B

2 an

d dr

ag t

hro

ugh

cel

l L2.

Ste

p 4:

Fir

st,c

lick

on

th

e 2

nex

t to

cel

l A2.

Th

en,c

lick

on

th

e bo

ttom

left

cor

ner

of

2an

d dr

ag d

own

th

rou

gh c

ell 1

2.S

tep

5:In

cel

l A1,

ente

r a

1 an

d pr

ess

EN

TE

R.

Pas

cal’s

tri

ang

le

Sh

eet

1S

hee

t 2

Sh

eet

3

Lesson 7-5

Exam

ple

Exer

cise

s

An

oth

er P

roo

f o

f P

yth

ago

rean

Th

eore

m

1.F

or r

igh

t tr

ian

gle

AB

Cw

ith

rig

ht

angl

e C

,an

d al

titu

de C �

D�as

sh

own

at

the

righ

t,n

ame

thre

e si

mil

ar t

rian

gles

.

�A

BC

��

AC

D�

�C

BD

2.L

ist

the

thre

e si

mil

ar t

rian

gles

as

hea

din

gs i

n

the

tabl

e be

low

.Use

th

e fi

gure

to

com

plet

e th

eta

ble

to l

ist

the

corr

espo

ndi

ng

part

s of

th

e th

ree

sim

ilar

rig

ht

tria

ngl

es.

3.U

se t

he

corr

espo

ndi

ng

part

s of

th

ese

sim

ilar

tri

angl

es a

nd

thei

r pr

opor

tion

s to

com

plet

e th

e st

atem

ents

in

th

e pr

oof

and

alge

brai

call

y pr

ove

the

Pyt

hag

orea

n T

heo

rem

.

Sta

tem

ents

Rea

son

s

1.R

igh

t tr

ian

gle

AB

Cw

ith

1.

Giv

enal

titu

te C �

D�.

2.�a c�

� �d a� ,

�b c��

� be �2.

Cor

resp

ondi

ng

part

s of

sim

ilar

tria

ngl

es a

re i

n t

he

sam

e ra

tio

3.a

2�

cd

,b2

� c

e3.

Cro

ss P

rodu

cts

4.a

2�

b2

� c

d�

b2

4.A

ddit

ion

Pro

pert

y of

Equ

alit

y

5.a

2�

b2

� c

d�

ce

5.S

ubs

titu

tion

6.a

2�

b2

� c

(d�

e)

6.D

istr

ibu

tion

Pro

pert

y

7.d

� e

� c

7.S

egm

ent

addi

tion

8.a2

�b2

�c2

8.S

ubs

titu

tion

A

ab

de

c

B

C D

Cha

pter

740

Gle

ncoe

Geo

met

ry

Enri

chm

ent

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

7-5


�A

BC

�A

CD

�C

BD

Sh

ort

Leg

ah

dL

on

g L

egb

eh

Hyp

ote

nu

sec

ba



Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com

panies, Inc.Chapter 7 Assessment Answer Key

Quiz 1 (Lessons 7–1 and 7–2) Quiz 3 (Lesson 7–4) Mid-Chapter TestPage 45 Page 46 Page 47

Quiz 2 (Lesson 7–3) Quiz 4 (Lesson 7–5)Page 45 Page 46

1.

2.

3.

4.

5.

1:30

33 in.

�BAC � �QPR or�ABC � �QPR by

SAS.

x � 4;scale factor 5:4

B

1.

2.

3.

4.

5.

yes; AA

No; the sides arenot proportional.

�ABD � �CDE or�ADB � �CDF;

8

22�12

� ft

6

1.

2.

3.

4.

5.

Not parallel because

�MJM

K� � �

NJN

L�

13�13

�

20

9

T(3, 2), U(3, �1)

1.

2.

3.

4.

5.

22�12

�

8.0 cm

corresp. altitudesare proportional tothe corresp. sides

5.3 cm

14

6.

7.

8.

9.

10.

No; SAS doesnot apply.yes; SAS

28; �83

�

120

3.6 in.

1.

2.

3.

4.

5.

B

J

C

J

B


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

An

swer

s

Chapter 7 Assessment Answer KeyVocabulary Test Form 1Page 48 Page 49 Page 50

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

ratio

scale factor

midsegment

extremes

means

false; similarpolygons

false; proportion

true

Sample answer:product of means isequal to product of

extremes

Sample answer:a segment with

endpoints that are themidpoints of any two

sides of a triangle

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

A

J

B

G

B

J

B

H

A

G

11.

12.

13.

14.

15.

16.

17.

18.

19.

B:

D

J

A

G

A

G

D

H

D

9.6


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com


Form 2A Form 2BPage 51 Page 52 Page 53 Page 54

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

A

F

D

H

B

H

C

F

C

G

11.

12.

13.

14.

15.

16.

17.

18.

B:

D

J

B

G

C

F

A

F

32

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

A

H

B

J

B

G

D

G

B

H

11.

12.

13.

14.

15.

16.

17.

18.

B:

D

F

C

J

B

F

D

H

26


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

An

swer

s

Chapter 7 Assessment Answer KeyForm 2CPage 55 Page 56

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

3:7

Yes; corres. �are �.

30 ft

18

42.5 ft

6.3

18.2

No; the sides arenot proportional.

72

�PQR � �STR

2�12

�

12.

13.

14.

15.

16.

17.

18.

B:

9.5

42

47

2

3

14.4

4

7


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com


Form 2DPage 57 Page 58

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

5:11

No; thecorresponding

sides and � arenot proportional.

48 ft

�43

�

183�13

� ft

5.5

15

yes; SSSSimilarity

75

�XYZ � �XNM

7.5

12.

13.

14.

15.

16.

17.

18.

B:

2.2

96

85

9.5

2

5�58

�

28

4.8


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

An

swer

s

Chapter 7 Assessment Answer KeyForm 3Page 59 Page 60

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

4:3

No; corr. sides arenot proportional.

yes; SAS

30 cm by 7.5 cm

5.85

5

104 in.

82

48

�83

�

5

12.

13.

14.

15.

16.

17.

18.

B:

11�37

�

7.2

�85

�

60

24.8

24 ft

9

25.6


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com


Extended-Response Test, Page 61Scoring Rubric

Score General Description Specific Criteria

• Shows thorough understanding of the concepts of ratios,properties of proportions, similar figures, similar triangles,dividing segments into parts, proportional parts of triangles,corresponding perimeters and altitudes, fractals, anditeration.

• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Figures are accurate and appropriate.• Goes beyond requirements of some or all problems.

• Shows an understanding of the concepts of ratios,properties of proportions, similar figures, similar triangles,dividing segments into parts, proportional parts oftriangles, corresponding perimeters and altitudes, fractals,and iteration.

• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Figures are mostly accurate and appropriate.• Satisfies all requirements of problems.

• Shows an understanding of most of the concepts of ratios,properties of proportions, similar figures, similar triangles,dividing segments into parts, proportional parts of triangles,corresponding perimeters and altitudes, fractals, anditeration.

• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Figures are mostly accurate.• Satisfies the requirements of most of the problems.

• Final computation is correct.• No written explanations or work is shown to substantiate

the final computation.• Figures may be accurate but lack detail or explanation.• Satisfies minimal requirements of some of the problems.

• Shows little or no understanding of most of the concepts ofratios, properties of proportions, similar figures, similartriangles, dividing segments into parts, proportional partsof triangles, corresponding perimeters and altitudes,fractals, and iteration.

• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Figures are inaccurate or inappropriate.• Does not satisfy requirements of problems.• No answer may be given.

0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given

1 Nearly Unsatisfactory A correct solution with nosupporting evidence orexplanation

2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem

3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation

4 SuperiorA correct solution that is supported by well-developed, accurateexplanations


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

An

swer

s

Chapter 7 Assessment Answer KeyExtended-Response Test, Page 61

Sample Answers

In addition to the scoring rubric found on page A26, the following sample answers may be used as guidance in evaluating open-ended assessment items.

1. �160� � �

53� or �

120� � �

135�

2. a. 3:2:2 (Note: Check to be sure that the sum of any two sides of thetriangle is greater than the third side. For example, a ratio of 1:1:2would not be acceptable.)

b. 18, 12, 12

c. 12, 8, 8

3. �ABH � �CDI � �GFI � �ADG � �GDE � �CFE � �AGE by the AAPostulate.

4.

5. a.

Mark the midpoint of each side of �PQR. Connect these points to form�XYZ. Since each segment of �XYZ is a midsegment of �PQR, itslength will be half the corresponding side, and therefore the perimeterwill be half the perimeter of �PQR.

b.

c. Each of the triangles are similar by SSS (since their sides are half thelength of the preceding sides), so the figure is strictly self-similar andthus a fractal.

d. 6

P R

Q

X

Y Z

P R

Q

X

Y Z

FD

CA

B

1

1E

4–3

3–4


Copyright ©

Glencoe/M

cGraw


he McG

raw-H

ill Com


Standardized Test PracticePage 62 Page 63

1.

2.

3.

4.

5.

6.

7. 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

8.

9.

10.

11.

12. F G H J

A B C D

F G H J

A B C D

F G H J

13.

14.

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

61 .

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

821 .

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0


Cop

yrig

ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

he M

cGra

w-H

ill C

ompa

nies

, In

c.

An

swer

s

Chapter 7 Assessment Answer KeyStandardized Test Practice (continued)Page 64

15.

16.

17.

18.

19.

20a.

20b.

20c.

�3

85.5

11 � x � 53

64.5 cm

congruent;TU � WX � �40�UV � XY � �53�VT � YU � �41�

ST � 6.32,PR � 28.46

slope of ST � �13

�,

slope of PR � �3

perpendicular

chapter 7 resource masters - crunchymath.weebly.com · teacher’s guide to using the chapter 7...

Documents