SAS Postulate. 4. none. 5. NSK. â. , AAS Theorem or ASA Postulate. 6. CBD. â. , AAS Theorem. 7. AAS Theorem. 8. SAS Postulate. 9. none. 10. HL The...

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Name ________________________ Unit 3 Test Review

Write the congruence statement and name the postulate/theorem used to prove the triangles are congruent. If they are not congruent, write none for both parts. L Y

1.

2.

3.

A

S

J

N

C

B W

∆NJL ≅ ____ Reason: ___________

∆WYZ ≅ ____ Reason: ___________

4.

A

R

K

X

Z

T

5.

C

K

M

∆ABC ≅ ____ Reason: ___________

6.

A

C

S B J

B

D

N E

∆ABD ≅ ____ Reason: ___________

∆MSJ ≅ ____ Reason: ___________

D

∆ABE ≅ ____ Reason: ___________

State the postulate or theorem that proves that the triangles are congruent. If the triangles cannot be proven congruent, write none. 8. DF || GE , DF ≅ GE 9. MJ || KN 7. ZY bisects ∠WYX , K ∠W ≅ ∠X Y D M F S

G W

N

X

Z

10. WY ⊥ WK , YZ ⊥ KZ , WK ≅ YZ W

J

E

11. NJ bisects ∠LNK , NJ bisects ∠LJK

12. ∠ZXW ≅ ∠VWX , ZX ≅ WV

L

K

Z

V R

J

N Y

Z

W K

X

13. MN and JK bisect each

14. DF || GE , ∠D ≅ ∠E

other.

D

15. YZ is the perpendicular bisector of WX

F

Y

K

M S

G J

E

W

N

Find the values of the variables. Show all work. 16. 17.

18.

x°

X

Z

x°

x°

52° y°

62° 2 y°

y°

75° 88°

19.

20.

21.

65°

y°

50°

2x + 7

3x − 2

y°

x° 4x − 5

x°

22.

23. y°

x°

110° x°

24. Given ABC≅DEF, m∠A = 55°, m∠B = 65°, AB = 18, DF = x + 6, and DE = 2x, find m∠F and AC.

25 Given: DA ⊥ AB , BC ⊥ DC , AB ≅ DC Prove: ∆DAB ≅ ∆BCD Statements

Reasons

26. Given: AB || DC , AB ≅ DC Prove: ∆ABD ≅ ∆CDB Statements

Reasons

A

B

D

C

A

B

D

C

27. Given: WZ ≅ XZ , Y is the midpoint of WX Prove: ∆WYZ ≅ ∆XYZ

Statements

Reasons

X

Z

K

M

28. Given: MN bisects JK , ∠M ≅ ∠N Prove: ∆MSJ ≅ ∆NSK

Statements

Y

W

S

Reasons

J

N

ANSWERS 1. ∆XYZ , HL Theorem 2. ∆JNK . SSS Postulate 3. ∆RTS , SAS Postulate 4. none 5. ∆NSK , AAS Theorem or ASA Postulate 6. ∆CBD , AAS Theorem 7. AAS Theorem 8. SAS Postulate 9. none 10. HL Theorem 11. ASA Postulate 12. SAS Postulate 13. SAS Postulate 14. AAS Theorem 15. SAS Postulate 16. x = 56, y = 23 17. x = 15, y = 75 18. x = 116, y = 64 19. x = 65, y = 80 20. x = 65, y = 50 21. x = 6 22. x = 40 23. x = 60, y = 30 24. m∠F = 60○, AC = 15 25. 1. DA ⊥ AB , BC ⊥ DC , AB ≅ DC 2. ∠ A and ∠ C are right angles 3. ∆ DAB and ∆ BCD are right ∆ s 4. BD ≅ BD 5. ∆DAB ≅ ∆BCD

1. 2. 3. 4. 5.

26. 1. AB || DC , AB ≅ DC 2. ∠ABD ≅ ∠CDB

1. Given 2. If lines, then alt. int. ∠ s ≅

3. BD ≅ BD 4. ∆ABD ≅ ∆CDB

Given Definition of perpendicular Definition of a right ∆ Reflexive Property HL Theorem

3. Reflexive Property 4. SAS Postulate

27. 1. 2. 3. 4.

WZ ≅ XZ , Y is the midpoint of WX WY ≅ XY ZY ≅ ZY ∆WYZ ≅ ∆XYZ

1. 2. 3. 4.

Given Definition of midpoint Reflexive Property SSS Postulate

28. 1. 2. 3. 4.

MN bisects JK , ∠M ≅ ∠N JS ≅ KS ∠MSJ ≅ ∠NSK ∆MSJ ≅ ∆NSK

1. 2. 3. 4.

Given Definition of bisect Vertical angles congruent AAS Theorem