Download Unit 10 Review

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.
4.
5.
6.
7.
8.
9.
11.
12.
_______ 2.
_______ 3.
_______ 4.
_______ 5.
_______ 6.
_______ 7.
_______ 8.
_______ 9.
_______ 10. 10.
_______ 11.
_______ 12.
_______ 13. 13.
14.
15.
16.
_______ 14.
_______ 15.
_______ 16.
Unit 10 Review Page 1
What additional congruence statement is needed to prove the triangles congruent by the
indicated postulate or theorem?
A
#17 – 20. Given: ∆NLY and ∆MPA
N
_________ 17. LN  PM , N  M by SAS
_________ 18. LN  PM , NY  MA by SSS
M
Y
L
_________ 19. L   P , LN  PM by AAS
P
_________ 20. L   P , M  N by ASA
#21 – 23. Given: ∆ABC and ∆DEF
C
_________ 21. A  D , AC  DF by ASA
_________ 22.  B  E , CB  FE by AAS
F
A
B
E
D
_________ 23. AC  DF , CB  FE by SAS
#24 – 26. Given: ∆QPR and ∆SPR
P
_________ 24. QR  SR , 3  4 by SAS
12
_________ 25. 1  2 , PR  PR by AAS
_________ 26. 1  2 , 3  4 by ASA
Q
34
S
R
Complete each statement using ∆ABC.
____________ 27. _?_ is the included side of A and  B .
____________ 28. The right angle is _?_.
A
____________ 29. The hypotenuse is _?_.
____________ 30. The side opposite A is _?_.
____________ 31. AB and _?_ are legs of the right triangle.
____________ 32. The angle opposite AC is _?_.
____________ 33. _?_ is the included angle of sides AC and CB .
B
C
For #27- 38
--------OMIT-------____________ 34. The
vertex angle is _?_.
____________ 35. The legs are _?_ and _?_.
____________
--------OMIT-------____________ 36. The
base is _?_.
Unit 10 Review Page 2
____________ 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: MS  LS , ES  BS
M
a) Mark the triangles with the given information.
B
1
b) What other corresponding parts are congruent?
S
2
E
L
c) Why are the triangles congruent?
40. Given: P is the midpoint of RS .  R  S
a) Mark the triangles with the given information.
b) What other corresponding parts are congruent?
R
T
P 1
2
S
V
c) Why are the triangles congruent?
d) Explain why T  V .
41. Given: TF  SM , F is the midpoint of SM .
T
a) Mark the triangles with the given information.
b) What other corresponding parts are congruent?
c) Why are the triangles congruent?
1 2
S
M
F
d) Explain why S  M .
Circle the correct answer choice.
R
42. Which of these will not be used as a reason in a proof of RT  RS ?
A) ASA
C) SAS
B) CPCTC
D) Reflexive Property
T
U
S
Unit 10 Review Page 3
Formal Proofs
F
A
3
43. Given: 1  2 , 3  4 , C is the midpoint of BE .
4
Prove: ∆ABC  ∆FEC
1
B
Statements
C
2
E
Reasons
A
B
44. Given: A  E , C is the midpoint of BD .
1
2
Prove: ∆ACB  ∆ECD
D
C
E
Statements
Reasons
A
45. Given: 1  2 , 3  4
Prove: ∆ABD  ∆CBD
Statements
B
1
2
3
4
D
C
Reasons
Unit 10 Review Page 4
A
46. Given: BC bisects ABD
BC bisects ACD
Prove: AC  DC
B
Statements
47. Given:
D
KS TR
S
Statements
C
Reasons
A , SAT  RAT
48. Given:
Prove: ST  RT
KR TS ,
Prove: SK  RT
3
4
1
2
K
R
S
R
A
T
Reasons
Statements
T
Reasons
Unit 10 Review Page 5
Review Answer Key
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
43.
17. NY  MA
45.
Statements
1. 1  2, 3  4, C is the
1. Given
midpoint of BE
2. BC  EC
3. ΔABC  ΔFEC
2. Def. of midpoint
3. AAS
44.
Statements
1. A  E, C is the midpoint of
1. Given
BD
2. BC  DC
3. 1  2
4. ΔACB  ΔECD
2. Def. of midpoint
3. Vertical angles
3. AAS
18. LY  PA
19. Y  A
Statements
1. 1  2, 3  4
20.
21.
22.
23.
46.
LN  PM
C  F
A  D
C  F
2. BD  BD
3. ΔABD  ΔCBD
1. BC bisects ABD,
26. PR  PR
BC bisects ACD
2. 1  2, 3  4
30. BC
31.
32.
33.
34.
BC
B
C
OMIT
AB, BC
OMIT
right
CPCTC (Congruent Parts of
Congruent Triangles are
Congruent)
39. (b) 1  2
(c) SAS
35.
36.
37.
38.
40. (b) RP  SP , 1  2
(c) ASA
(d) CPCTC
41. (b) 1  2, SF  MF, TF  TF
(c) SAS
(d) CPCTC
42. A
Reasons
Reasons
1. Given
2. Reflexive property
3. ASA
Statements
24. PR  PR
25. Q  S
27. AB
28. B
29. AC
Reasons
3. BC  BC
4. ΔABC  ΔDBC
5. AC  DC
Reasons
1. Given
2.
3,
4.
5.
Def. of angle bisector
Reflexive property
ASA
CPCTC
47.
Statements
1. KR TS, KS TR
2. KRS  TSR, KSR  TRS
3. SR  SR
4. ΔSKR  ΔRTS
5. SK  RT
Reasons
1. Given
2.
3,
4.
5.
Alternate interior angles
Reflexive property
ASA
CPCTC
48.
1.
Statements
A , SAT  RAT
Reasons
1. Given
2. SA  RA
2. Radii are congruent
3. AT  AT
4. ΔSAT  ΔRAT
5. ST  RT
3, Reflexive property
4. SAS
5. CPCTC
Unit 10 Review Page 6