Name______Period______Date______

Unit 10 – Review

Can the triangles be proved congruent? If so, name the postulate or theorem that would prove the triangles congruent. If not, write NONE. Mark vertical angles or shared sides as necessary.

______1. 1. 2. 3.

______2.

______3.

______4. 4. 5. 6.

______5.

______6.

______7. 7. 8. 9.

______8.

______9.

______10. 10. 11. 12.

______11.

______12.

______13. 13. 14. 15. 16.

______14.

______15.

______16.

What additional congruence statement is needed to prove the triangles congruent by the indicated postulate or theorem?

#17 – 20. Given: ∆NLY and ∆MPA

______17. , by SAS

______18. , by SSS

______19. , by AAS

______20. , by ASA

#21 – 23. Given: ∆ABC and ∆DEF

______21. , by ASA

______22. , by AAS

______23. , by SAS

#24 – 26. Given: ∆QPR and ∆SPR

______24. , by SAS

______25. , by AAS

______26. , by ASA

Complete each statement using ∆ABC.

______27. _?_ is the included side of and .

______28. The right angle is _?_.

______29. The hypotenuse is _?_.

______30. The side opposite is _?_.

______31. and _?_ are legs of the right triangle.

______32. The angle opposite is _?_.

______33. _?_ is the included angle of sides and .

______34. The vertex angle is _?_.

______35. The legs are _?_ and _?_.

______

______36. The base is _?_.

______37. If you use perpendicular segments as a statement in a proof, in the next

statement you should name the _?_ angles formed.

______38. After two triangles are proven congruent, the definition that allows you to state the remaining parts congruent is _?_.

Informal Proofs.

39. Given: ,

a) Mark the triangles with the given information.

b) What other corresponding parts are congruent?

c) Why are the triangles congruent?

40. Given: P is the midpoint of .

a) Mark the triangles with the given information.

b) What other corresponding parts are congruent?

c) Why are the triangles congruent?

d) Explain why.

41. Given: , F is the midpoint of .

a) Mark the triangles with the given information.

b) What other corresponding parts are congruent?

c) Why are the triangles congruent?

d) Explain why.

Circle the correct answer choice.

42. Which of these will not be used as a reason in a proof of ?

A) ASA C) SAS

B) CPCTC D) Reflexive Property

Formal Proofs

43. Given: , , C is the midpoint of .

Prove: ∆ABC∆FEC

44. Given: , C is the midpoint of .

Prove: ∆ACB∆ECD

45. Given: ,

Prove: ∆ABD∆CBD

46. Given: bisects

bisects

Prove:

Unit 10 Review Page 4

47. Given: ,

Prove:

48. Given: ,

Prove:

Unit 10 Review Page 4

Review Answer Key

Unit 10 Review Page 4

1. ASA

2. HL

3. AAS

4. AAS

5. SSS

6. SAS

7. SAS

8. AAS

9. SAS

10. ASA

11. NONE

12. NONE

13. SAS

14. SAS

15. ASA

16. SSS

17.

18.

19. ÐY @ ÐA

20.

21. ÐC @ ÐF

22. ÐA @ ÐD

23. ÐC @ ÐF

24.

25. ÐQ @ ÐS

26.

27.

28. ÐB

29.

30.

31.

32. ÐB

33. ÐC

34. OMIT

35.

36. OMIT

37. right

38. CPCTC (Congruent Parts of Congruent Triangles are Congruent)

39. (b) Ð1 @ Ð2

(c) SAS

40. (b) , Ð1 @ Ð2

(c) ASA

(d) CPCTC

41. (b) Ð1 @ Ð2,

(c) SAS

(d) CPCTC

42. A

43.

Statements / Reasons
1. Ð1 @ Ð2, Ð3 @ Ð4, C is the midpoint of / 1. Given
2. / 2. Def. of midpoint
3. ΔABC @ ΔFEC / 3. AAS

44.

Statements / Reasons
1. ÐA @ ÐE, C is the midpoint of / 1. Given
2. / 2. Def. of midpoint
3. Ð1 @ Ð2 / 3. Vertical angles
4. ΔACB @ ΔECD / 3. AAS

45.

Statements / Reasons
1. Ð1 @ Ð2, Ð3 @ Ð4 / 1. Given
2. / 2. Reflexive property
3. ΔABD @ ΔCBD / 3. ASA

46.

Statements / Reasons
1. bisects ÐABD,
bisects ÐACD / 1. Given
2. Ð1 @ Ð2, Ð3 @ Ð4 / 2. Def. of angle bisector
3. / 3, Reflexive property
4. ΔABC @ ΔDBC / 4. ASA
5. / 5. CPCTC

47.

Statements / Reasons
1. / 1. Given
2. ÐKRS @ ÐTSR, ÐKSR @ ÐTRS / 2. Alternate interior angles
3. / 3, Reflexive property
4. ΔSKR @ ΔRTS / 4. ASA
5. / 5. CPCTC

48.

Statements / Reasons
1. , ÐSAT @ ÐRAT / 1. Given
2. / 2. Radii are congruent
3. / 3, Reflexive property
4. ΔSAT @ ΔRAT / 4. SAS
5. / 5. CPCTC

Unit 10 Review Page 4