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Lesson 5.1 Assignment

Name Date

We Like to Move It!Translating, Rotating, and Reflecting Geometric Figures

1. Transform rectangle JKLM so it sits in the shaded rectangle in Quadrant III.

216 212 28 24 0 4

4

24

28

212

216

8

12

16

8 12 16x

y

LM

KJ

a. How many different transformations will it take to place rectangle JKLM in the shaded areain Quadrant III?

b. Describe and perform a transformation to move rectangle JKLM to Quadrant II. Identify the coordinates of the vertices of the transformed rectangle, J9K9L9M9. Explain how you determined your answer.

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c. Describe and perform the transformation that can be used to move rectangle J9K9L9M9 to Quadrant III. Identify the coordinates of the vertices of the transformed rectangle, J0K0L0M0. Explain how you determined your answer.

d. Could a different transformation(s) be used to move rectangle JKLM to Quadrant III? Explain your reasoning.

2. Consider figure QRST.

216 212 28 24 0 4

4

24

28

212

216

8

12

16

8 12 16x

y

T S

Q R

Ramona states that there are three ways to transform QRST to place its image in the shaded area in Quadrant II.

• Translate QRST vertically 13 units up, then horizontally 15 units to the left.

• Reflect QRST over the x-axis then over the y-axis.

• Rotate QRST 180° counterclockwise (or clockwise) about the origin.

Lesson 5.1 Assignment page 2

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Lesson 5.1 Assignment page 3

Name Date

a. Without graphing, determine the coordinates of the vertices of the image for each of the transformations Ramona listed. Explain how you determined your answers.

b. Which transformation would you recommend that Ramona choose? Explain your reasoning.

c. Perform the transformation you chose in part (b).

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Hey, Haven’t I Seen You Before?Congruent Triangles

1. Analyze triangle ABC.

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2

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6

8

4 6 8x

y

B

AC

a. Describe a transformation that can be performed on n ABC that will result in a triangle being created in Quadrant I.

b. Will the transformation you described preserve the size and shape of the triangle? Explain your reasoning.

c. Perform the transformation and name the new triangle DEF.

d. List the coordinates for the vertices of both triangles.

e. Using the names of the vertices, write a triangle congruence statement for the triangles.

Lesson 5.2 Assignment

Name Date

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Lesson 5.2 Assignment page 2

f. Using your congruence statement, identify the congruent angles.

g. Using your congruence statement, identify the congruent sides.

2. Analyze triangle MNO.

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4

6

8

4 6 8x

y

N

M

O

a. Describe a transformation that can be performed on n MNO that will result in a triangle being created in Quadrant III.

b. Will the transformation you described preserve the size and shape of the triangle?

c. Perform the transformation and name the new triangle PQR.

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d. List the coordinates for the vertices of both triangles.

e. Using the names of the vertices, write a triangle congruence statement for the triangles.

f. Using your congruence statement, identify the congruent angles.

g. Using your congruence statement, identify the congruent sides.

Lesson 5.2 Assignment page 3

Name Date

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It’s All About the SidesSide-Side-Side Congruence Theorem

1. Analyze the triangles shown.

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R

T

S

L

K

J

a. Are the two triangles shown on the grid congruent? Show and explain how you determined your answer.

Lesson 5.3 Assignment

Name Date

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b. Juan says the triangle congruency statement for these triangles should be nJKL > nRST. Natsu says the triangle congruency statement for these triangles should be nJKL > nSRT. Who is correct? Explain your reasoning.

Lesson 5.3 Assignment page 2

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Lesson 5.4 Assignment

Name Date

Make Sure the Angle Is IncludedSide-Angle-Side Congruence Theorem

1. Analyze the triangles shown.

28 26 24 22 0

2

22

24

26

28

4

6

8

4 6 8x

y

N

O

M

K

J L

a. Use the distance formula and a protractor to prove that the two triangles shown on the grid are congruent by SAS. Show your work.

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b. Mark the triangles to show which sides and angles are congruent.

c. Write a congruency statement for the triangles.

Lesson 5.4 Assignment page 2

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Lesson 5.5 Assignment

Name Date

Angle to the Left of Me, Angle to the Right of MeAngle-Side-Angle Congruence Theorem

1. Emerson wants to translate n ABC and then reflect it over the y-axis to form a new triangle in Quadrant II. She uses what she knows about transformations to determine the vertices of n A9B9C9 before performing the transformations.

28 26 24 22 0 2

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6 8x

y

A

C

B

A9

B9

C9

a. Briefly describe how Emerson can use the ASA Congruence Theorem to determine whether or not she transformed n ABC, such that the image is congruent to the pre-image.

b. Connect points A9, B9, and C9. Use a protractor to determine the measure of two corresponding angles in each triangle.

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c. Calculate the length of the included side of n ABC and n A9B9C9. Show your work.

d. Did Emerson perform the transformations on n ABC so that the image is congruent to the pre-image? Explain your reasoning.

Lesson 5.5 Assignment page 2

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Lesson 5.6 Assignment

Name Date

Sides Not IncludedAngle-Angle-Side Congruence Theorem

1. Describe and use AAS to prove that triangle LMN is congruent to triangle QRS.

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26

28

4

6

8

6 8x

y

QS

R

N

M

L

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2. Triangles ABC and DFG are given.

90°

39°

90°51°

A

B C

D

F G

a. Side BC of n ABC is congruent to side FG of nDFG. Mark the triangles to show that these sides are congruent.

b. Do you have enough information to determine whether n ABD is congruent to nDFG? Explain your reasoning.

c. Without using a protractor, calculate the measure of /BAC. Show your work. Write the measure on the triangle.

d. Now, do you have enough information to determine that n ABC is congruent to nDFG? Write congruence statements to justify your reasoning.

Lesson 5.6 Assignment page 2

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Lesson 5.7 Assignment

Name Date

Any Other Theorems You Forgot to Mention?Using Congruent Triangles

1. Use triangle congruency proofs to prove the statement using the given information.

a. A

B

C D E

Given: /A > /E

___

AB>___

EC

Prove:___

CB>___

DC

b. A

BC

D

EF

Given: ___

FE>___

BC

___

AFi___

CD, ___

ABi___

ED

Prove: nABF > nDEC

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Lesson 5.7 Assignment page 2

c. A

B C D

E Given: nABC is equilateral

___

ACi___

ED

___

AB>___

ED

Prove: /E > /ACD

d. A

B D C

Given: ___

ADis a perpendicular bisector of ___

BC

___

AB>___

AC

Prove: nABD > nACD

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Lesson 5.7 Assignment page 3

Name Date

e. E F

A

B

C D

Given: ‹

___ › EF i

___ AD

___

BCis angle bisector of /ABD

___

BC is the perpendicular bisector of ‹

___ › EF

Prove:nCAB> nCDB

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Lesson 5.7 Assignment page 4

2. Write the information needed in each situation to prove that the triangles are congruent, and state the postulate, or state that there is already enough information to prove the specified triangles congruent, and state the postulate.

a.

C

B

A

D

Given: /B > /D

Prove: nABC > nADC

b. E C

A1

23

B D

Given:/BAC>/DAE

___

AE > ___

AC

Ais the midpoint of___

BD

Prove: nBEA > nDCA

c. B

AD

C

P

Given: /A and /D are right angles

Prove: nBAP > nCDP

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