Evaluate: Homework and Practice

Evaluate: Homework and Practice Decide whether you have enough information to determine that the triangles are congruent. If they are congruent, explain why. 1.

B

A

D

C

4.

F

F

C

E D

A

D

A

B

C

B

C

A

6.

E

D

F

B

E

F

B

C

A

5.

D

A

F

E

3.

B

2.

E

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D

C

F

E

Each diagram shows two triangles with two congruent angles or sides. Identify one additional pair of corresponding angles or sides such that, if the pair were congruent, the two triangles could be proved congruent by AAS. 7.

E

B A

C

F

E

E

A C

B D

F

E

10.

F

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A

9.

D

8.

B A B

C

D

B

12. E

A

A

C

Module 6

F D

D

B

11.

C

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C

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Lesson 2

13. Complete the proof. ‹ › −   bisects ∠BCD. Given: ∠B ≅ ∠D, ​  AC ​    

B

Prove: △ABC ≅ △ADC

A

C

D

Statements

Reasons

_ _ 1. AC​ ​  ≅ AC​ ​   ‹ › − 2. ​  AC ​       bisects ∠BCD.

2. Given

3.

3. Definition of angle bisector

4.

4. Given

5. △ABC ≅ △ADC

5.

1.

14. Write a two-column proof or a paragraph proof. _ _ _ _ ∥DE​ ​   , CB​ ​  ≅ CD​ ​   . Given: ​AB​  A Prove: △ABC ≅ △EDC

D B

E

Reasons

Statements

© Houghton Mifflin Harcourt Publishing Company

C

Each diagram shows △ABC and △DEF on the coordinate plane, with ∠A ≅ ∠E, and ∠C ≅ ∠F. Identify whether the two triangles are congruent. If they are not congruent, explain how you know. If they are congruent, find the length of each side of each triangle. 15.

A

16.

y

y

C

4 B -4

C 2 -2

D 0

B 2

E 4

x

-4

1 E

-2

A x

F 4

F D

Module 6

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Lesson 2