Geometry 1A
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