geometry-a · 2020. 5. 31. · brownsville independent school district 1900 price road,...

Geometry-A

Student Name: __________________

Student ID: _____________________

School Name: ___________________

Summer School 2020Distance Learning

Packet

Teacher Name: __________________

High School Math

Brownsville Independent School District

1900 Price Road, Brownsville, TX 78521, (956) 548-8000 www.bisd.us

May 2020

Esteemed Parents and Family Members,

We hope this letter finds you safe and healthy amid this uneasy time of COVID-19. As always, our priority is

the safety and welfare of our students. Our 2020 summer program will continue by utilizing virtual learning

platforms and will begin on June 1 and end on June 18, 2020. The purpose of the summer program is to

provide students the opportunity to gain credit for the course your student has failed.

You have received this summer 2020 instructional packet for your (9th - 12th grade) student. This instructional

packet includes materials for the core area(s) your student has failed.

We ask that you contact your student’s school to:

• give you the failing subject area(s)

• give you your student’s summer teachers’ name and contact information / email address

• update any contact information including any changes and additional contact numbers, and

email addresses, etc.

• receive login information for the digital platform

The platform utilized this summer will be:

• 9th -12th Google Classroom

(Download Google Classroom app or access through the Clever Portal)

Our sincere hope is that your child will participate and take advantage of this opportunity for promotion that

will greatly support your child’s area(s) of educational need.

Please encourage your student to read, watch educational programs, and practice their writing and speaking

skills. This is also a great time to share family stories and traditions, play board games and enjoy family time.

As always, it is an honor to continue to serve you and we value your family's commitment in entrusting us with

your child's education.

BISD does not discriminate on the basis of race, color, national origin, gender, religion, age, or disability or genetic information in employment

or provision of services, programs, or activities.

Brownsville Independent School District

1900 Price Road, Brownsville, TX 78521, (956) 548-8000 www.bisd.us

Mayo de 2020

Estimados Padres y Miembros de Familia,

Esperamos que esta carta le encuentre a buen resguardo y en buena salud durante estos días difíciles del

COVID-19. Como siempre, nuestra prioridad es la seguridad y el bienestar de nuestros estudiantes. Nuestro

programa de verano 2020 continuará utilizando plataformas de aprendizaje virtuales y comenzará el 1 de junio

y terminará el 18 de junio de 2020. El propósito del programa de verano es proporcionar a los estudiantes que

no fueron promovidos al siguiente grado, una oportunidad para obtener la promoción.

Con el fin de trabajar en la promoción de su hijo/a al siguiente grado, usted ha recibido un paquete de

instrucción para el verano del 2020 para su hijo/a de preparatoria. Dicho paquete incluye materiales para la(s)

asignatura(s) que su hijo/a reprobó.

Le pedimos que se ponga en contacto con la escuela de su hijo/a para:

• darle el área(s) de materia(s) que está reprobando.

• darle el nombre del maestro/a de verano de su hijo/a y su correo electrónico

• actualizar cualquier información de contacto, incluyendo cualquier cambio y números

de contacto adicionales, y correo electrónico, etc.

• recibir la información para conectarse a las plataformas digitales

La siguiente plataforma virtual se utilizará este verano para la preparatoria:

• Google Classroom

(Descargar aplicación de Google Classroom o usar el portal de Clever)

Esperamos sinceramente que su hijo/a participe y aproveche esta oportunidad de promoción que apoyará en

gran medida las áreas de su necesidad educativa.

Anime a sus hijos/as a leer, ver programas educativos y practicar sus habilidades para escribir y hablar. Este es

también un gran momento para compartir historias y tradiciones familiares, jugar juegos de mesa y disfrutar

del tiempo en familia.

Como siempre, es un honor continuar sirviéndole y valoramos nuestro compromiso con su familia al

confiarnos la educación de su hijo/a.

BISD no discrimina de acuerdo de raza, color, origen nacional, género, religión, edad, información genética, o incapacidad en el empleo o en

la provisión de servicios, programas o actividades.

Geometry-A Summer 2020

Lesson TEK Description TEK Resources Pearson Realize

Week 1(June 1-June 5) T1L3 Measuring Angles G.6A T1-Lesson 3

T1L4 Exploring Angle Pairs G.6A T1-Lesson 4

T3L1 Lines and Angles G.6A T3-Lesson 1

Week 2 (June 7-June 12) T3L7 Equations of Lines in the

Coordinate Plane G.2B T3 Lesson 7

T3L8 Slopes of Parallel and Perpendicular Lines G.2C T3 Lesson 8

T4L2 Triangle Congruence by SSS and SAS G.6B T4 Lesson 2

Week 3 (June 15-June 18) T4L3 Triangle Congruence by ASA and

AAS G.6B T4 Lesson 3

T4L6 Congruence in right Triangles G.6B T4 Lesson 6

Finalize all assignments

Geometry-A

Student Name: __________________

Student ID: _____________________

School Name: ___________________

Summer School 2020

Week 1

Teacher Name: __________________

High School Math

Name Class

Date

1-3 Practice Form G

Use the diagram below for Exercises 1–11. Find the measure of each angle.

Classify each angle as acute, right, obtuse, or straight.

6. ∠MLN 7. ∠NLO 8. ∠MLP

9. ∠OLP 10. ∠OLQ 11. ∠MLQ

Use the figure at the right for Exercises 12 and 13.

12. What is another name for ∠XYW?

13. What is another name for ∠WYZ?

Use a protractor. Measure and classify each angle.

14. 15. 16.

17. 18.

Pearson Texas Geometry

Measuring Angles

1. ∠MLN

2. ∠NLP

3. ∠NLQ

4. ∠OLP

5. ∠MLQ

Name Class

Date

1-3

Practice (continued) Form G

19. ∠JKL and∠CDE are congruent. If m∠JKL = 137, what is m∠CDE?

Use the figure at the right for Exercises 20–23. m∠FXH = 130 and m∠FXG = 49.

20. ∠FXG ≅

21. m∠GXH =

22. Name a straight angle in the figure.

23. ∠IXJ ≅

24. Algebra If m∠RZT = 110, m∠RZS = 3s, andm∠TZS = 8s, what are m∠RZS and m∠TZS?

25. Algebra m∠OZP = 4r + 2, m∠PZQ = 5r − 12, andm∠OZQ = 125. What are m∠OZP and m∠PZQ?

26. Reasoning Elsa draws an angle that measures 56. Tristan draws a congruent angle.Tristan says his angle is obtuse. Is he correct? Why or why not?

27. Lisa makes a cherry pie and an apple pie. She cuts the cherry pie into six equal wedgesand she cuts the apple pie into eight equal wedges. How many degrees greater is themeasure of a cherry pie wedge than the measure of an apple pie wedge?

28. Reasoning ∠JNR and ∠RNX are congruent. If the sum of the measures of the twoangles is 180, what type of angle are they?

29. A new pizza place in town cuts their circular pizzas into 12 equal slices. What is themeasure of the angle of each slice?

Measuring Angles

Name Class

Date

1-4 Practice

Use the diagram at the right. Is each statement true? Explain.

1. ∠2 and ∠5 are adjacent angles.

2. ∠1 and ∠4 are vertical angles.

3. ∠4 and ∠5 are complementary.

Name an angle or angles in the diagram described by each of the following.

4. complementary to ∠BOC

5. supplementary to ∠DOB

6. adjacent and supplementary to ∠AOC

Use the diagram below for Exercises 7 and 8. Solve for x. Find the angle measures.

7. m∠AOB = 4x − 1; m∠BOC = 2x + 15; m∠AOC = 8x + 8

8. m∠COD = 8x + 13; m∠BOC = 3x − 10; m∠BOD = 12x − 6

9. ∠ABC and ∠EBF are a pair of vertical angles; m∠ABC = 3x + 8 and m∠EBF= 2x + 48. What are m∠ABC and m∠EBF?

10. ∠JKL and ∠MNP are complementary; m∠JKL = 2x − 3 andm∠MNP = 5x + 2. What are m∠JKL and m∠MNP?

For Exercises 11–14, can you make each conclusion from the information in the diagram? Explain.

11. ∠3 ≅ ∠4 12. ∠2 ≅ ∠4

13. m∠1 + m∠5 = m∠3 14. m∠3 = 90

15. bisects ∠JKL. If m∠JKM = 86, what is m∠JKL?

16. bisects ∠RST. If m∠RST = 62, what is m∠RSV?

Pearson Texas Geometry

Exploring Angle Pairs

Form G

Name Class

Date

1-4 Practice (continued) Form G

bisects ∠PQR. Solve for x and find m∠PQR.

17. m∠PQS = 3x; m∠SQR = 5x − 20

18. m∠PQS = 2x + 1; m∠RQS = 4x − 15

19. m∠PQR = 3x − 12; m∠PQS = 30

20. m∠PQS = 2x + 10; m∠SQR = 5x − 17

For Exercises 21–24, can you make each conclusion from the information in the diagram below? Explain.

21. ∠DAB and ∠CDB are congruent.

22. ∠ADB and ∠CDB are complementary.

23. ∠ADB and ∠CDB are congruent.

24. ∠ADB and ∠BCD are congruent.

25. Algebra ∠MLN and ∠JLK are complementary, m∠MLN = 7x − 1, andm∠JLK = 4x + 3.a. Solve for x.b. Find m∠MLN and m∠JKL.c. Show how you can check your answer.

26. Reasoning Describe all the situations in which the following statements aretrue.a. Two vertical angles are also complementary.b. A linear pair is also supplementary.c. Two supplementary angles are also a linear pair.d. Two vertical angles are also a linear pair.

27. Open-Ended Write and solve an equation using an angle bisector to find themeasure of an angle.

Pearson Texas Geometry Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.

Exploring Angle Pairs

Name Class Date

3-1 Practice Form G

Use the diagram to name each of the following.

1. a pair of parallel planes

2. all lines that are parallel to

3. four lines that are skew to

4. all lines that are parallel to plane QUVR

5. a plane parallel to plane QUWS

In Exercises 6–11, describe the statement as true or false. If false, explain.

6. and are skew lines. 7. plane DBF ║plane ABD

8. ║ 9. ║

10. plane EFH ║ plane ABD 11. and are skew lines.

12. You are driving over a bridge that runs east to west. Below the bridge, a highway runsnorth to south. Are the bridge and the highway parallel, skew, or neither? Explain.

13. Open-Ended List parts of your classroom that fit each description below.

a. parallel to the top of a window

b. skew with one side of the door

c. parallel to the plane of the floor

14. Reasoning Your friend says that the sides of a ladder and the rungs of a ladder areskew. Is this true? Explain.

15. Visualization If two planes are parallel, must all lines within those planes beparallel? Explain.


Lines and Angles

Name Class Date

3-1


Identify all pairs of each type of angle in the diagram below right.

16. corresponding angles

17. same-side interior angles

18. alternate interior angles

19. alternate exterior angles

Decide whether the angles are alternate interior angles, same-side interior angles, corresponding angles, or alternate exterior angles.

20. ∠2 and ∠7 21. ∠5 and ∠4

22. ∠8 and ∠3 23. ∠6 and ∠4

24. ∠1 and ∠5

25. Draw a Diagram Line e intersects trapezoid ABCD. Sketch a diagram thatmeets the following conditions.

a. and are parallel.

b. ∠1 and ∠6 are alternate exterior angles.

c. ∠2 and ∠3 are same-side interior angles.

d. ∠4 and ∠5 are each supplementary to ∠3.

26. Writing Describe three real-world objects that represent two linesintersected by a transversal.

27. The map at the right shows the intersection ofMaple Street and Oak Street by Main Street.Name the angle pairs represented by thelocations listed below.

a. town hall and gas station

b. school and library

c. library and post office

d. school and gas station


Lines and Angles

Geometry-A

Student Name: __________________

Student ID: _____________________

School Name: ___________________

Summer School 2020

Week 2

Teacher Name: __________________

High School Math

Name Class Date

3-7 Practice Form G

Find the slope of the line passing through the given points.

1. 2.

3. (2, 3), (−1, −6) 4. (−6, −2), (−3, −6) 5. (2, 9), (4, −7)

Graph each line.

6. y = 3x − 4 7. y − 2 = (x + 3) 8. y + 2 = −4(x + 3)

Use the given information to write an equation for each line.

9. slope 6, y-intercept 4 10. slope − , y-intercept −2

11. 12.

13. through (−2, 0) and (3, 10) 14. through (10, 2) and (2, −2)

Equations of Lines in the Coordinate Plane

Name Class Date


Graph each line.

15. y = −4 16. x = 3 17. y = 5

18. Open-Ended Write equations for three lines that contain the point (0, 2).

Write each equation in slope-intercept form.

19. y − 3 = 4(x + 2) 20. y − 2 = −2(x − 5) 21. y +1 = (x + 4)

22. A wireless phone company charges $20 for a basic plan eachmonth plus $0.25/min for each call.a. Write an equation to show how much the company

charges, where x is the number of minutes used and y isthe total cost.

b. Find the total cost for 300 minutes, 350 minutes, and 400minutes.

c. Graph the equation using the values for 300 and 400minutes.

Graph each pair of lines. Then find their point of intersection.

23. y = −5, x = −2 24. y = 6, x = −1

Equations of Lines in the Coordinate Plane


Name Class Date

3-8

Practice Form G

In Exercises 1 and 2, are lines m1 and m2 parallel? Explain. 1.

1. 2.

Write an equation of the line parallel to that contains point C.

3. : y = −5x + 12; C(−2, 1) 4. : y = 47 x + 7 2

7 ; C(7, 1)

5. : y = 15 x + 8 4

5 ; C(3, 6) 6. : y = − 25 x + 5 2

5 ; C(5, −2)

In Exercises 7 and 8, are lines m1 and m2 perpendicular? Explain.

7. 8.

Write an equation of the line perpendicular to the given line that contains P.

9. P(−6, 5); y = 2x − 3 10. P(4, 3); y = −3x − 15

11. P(−6, −3); y = x− 1 12. P(5, 5); y = 74 x + 11 1

2


Slopes of Parallel and Perpendicular Lines

Name Class Date

3-8


13. The line that represents the right boundary of astreet is shown on the grid at the right.a. What is the equation of the left boundary,

which is parallel to the right boundary, andpasses through point L(200, 100)?

b. Graph the left boundary.

Rewrite each equation in slope intercept form. Then determine whether the lines are parallel. Explain.

14. 2y = x + 15 15. 10y + 130 = 50x 16. 2y = 15 + 4xx = 2y + 5 −5y = 2x + 11 6y − 30 = 12x

Rewrite each equation in slope-intercept form. Then determine whether the lines are perpendicular. Explain.

17. y − 1 = −x −6 18. 3 14 46y x− = − 19. 5

26 ( 4)y x− = − + 563 ( 5)y x− = − − 2y = 8x + 18 5y = 2x + 6

20. A town’s building code states that stairs and rampsmust have a handrail. The sketch at the right has ascale of 7 in. to each grid space.a. The handrail needs to be at least 35 in. above the

ramp. Mark the point 35 in. above the top of theramp. What are its coordinates?

b. What is the equation of the line for thehandrail?


Slopes of Parallel and Perpendicular Lines

Name Class Date

4-2 Practice Form G

Draw ∆MGT. Use the triangle to answer the questions below.

1. What angle is included between GM and MT ?

2. Which sides include T∠ ?

3. What angle is included between GT and MG ?

Would you use SSS or SAS to prove the triangles congruent? If there is not enough information to prove the triangles congruent by SSS or SAS, write not enough information. Explain your answer.

4. 5. 6.

7. 8. 9.

10. 11. 12.


Triangle Congruence by SSS and SAS

Name Class Date


13. Draw aDiagram A student draws ∆ABC and ∆QRS. The following sides and angles arecongruent:

AC QS≅ AB QR≅ ∠B ≅ ∠R

Based on this, can the student use either SSS or SAS to prove that ∆ABC ≅ ∆QRS? If the answer is no, explain what additional information the student needs. Use a sketch to help explain your answer.

14. Given: ,BC DC AC EC≅ ≅

Prove: ∆ABC ≅ ∆EDC

15. Given: || , ≅WX YZ WX YZProve: ∆WXZ ≅ ∆YZX

16. Error Analysis ∆FGH and ∆PQR are both equilateral triangles. Your friend says thismeans they are congruent by the SSS Postulate. Is your friend correct? Explain.

17. A student is gluing same-sized toothpicks together to make triangles. She plans to use thesetriangles to make a model of a bridge. Will all the triangles be congruent? Explain youranswer.


Triangle Congruence by SSS and SAS

Statements Reasons

Geometry-A

Student Name: __________________

Student ID: _____________________

School Name: ___________________

Summer School 2020

Week 3

Teacher Name: __________________

High School Math

Name two triangles that are congruent by ASA.

1. 2.

3. Developing Proof Complete the proof by filling in the blanks.Given: ∠HIJ ≅ ∠KI

∠IJH ≅ ∠IJKProve: ∆HIJ ≅ ∆KIJProof: ∠HIJ ≅ ∠KIJ and ∠IJH ≅ ∠IJK are given.

≅ by .So, ∆HIJ ≅ ∆KIJ by .

4. Given: ∠LOM ≅ ∠NPM, ≅

Prove: ∆LOM ≅ ∆NPM

5. Given: ∠B and ∠D are right angles. bisects

Prove: ∆ABC ≅ ∆EDC


Class Date Name

Practice Form G 4-3 Triangle Congruence by ASA and AAS

6. Developing Proof Complete the proof.

Given: ∠1 ≅ ∠2, AB ⊥ BL , KL ⊥ BL , AB ≅ KL

Prove: ∆ABG ≅ ∆KLG

Proof:

7. Write a flow proof.

Given: ∠E ≅ ∠H

∠HFG ≅ ∠EGF

Prove: ∆EGF ≅ ∆HFG

8. Write a two-column proof.

Given: ∠K ≅ ∠MKL ≅ ML

Prove: ∆JKL ≅ ∆PML

For Exercises 9 and 10, write a paragraph proof.

9. Given: ∠D ≅ ∠GHE ≅ FE

Prove: ∆EFG ≅ ∆EHD

10. Given: JM bisects ∠J.JM ⊥ KL

Prove: ∆JMK ≅ ∆JML


Name Class Date

Practice (continued) Form G 4-3 Triangle Congruence by ASA and AAS

Name Class Date

4-6 Practice Form G

1. Developing Proof Complete the paragraph proof.

Given:

Prove: ∆RUT ≅ ∆RST

Proof: It is given that . So, _____ and _______are_______ anglesbecause perpendicular lines form ______ angles. _______ ≅ by the Reflexive Property of Congruence. It is given that _______ ≅ . So, ∆RUT ≅ ∆RST by _______.

2. Look at Exercise 1. If m∠RST = 46, what is m∠RUT?

3. Write a flow proof. Use the information from the diagram to prove that

∆ABD ≅ ∆CDB.

4. Look at Exercise 3. Can you prove that ∆ABD ≅ ∆CDB without using theHypotenuse-Leg Theorem? Explain.

Construct a triangle congruent to each triangle by the Hypotenuse-Leg Theorem.

5. 6.


Congruence in Right Triangles

Name Class Date


Algebra For what values of x or x and y are the triangles congruent by HL?

7. 8.

9. 10.

11. Write a paragraph proof.

Given: bisects ∠ECD, ∠ACB are right angles.

Prove: ∆ACB ≅ ∆DCE

What additional information would prove each pair of triangles congruent by the Hypotenuse-Leg Theorem?

12. 13.

14. 15.

16. Reasoning Are the triangles congruent?Explain.


Congruence in Right Triangles

geometry-a · 2020. 5. 31. · brownsville independent school district 1900 price road,...

Documents