Geometry Ch 4 Post test
____
1. Can you use the SAS Postulate, the AAS Theorem, or both to prove the triangles congruent?
A. either SAS or AAS
B. AAS only
____
C. SAS only
D. neither
2. Which triangles are congruent by ASA?
F
A
(
V
T
((
G
(
)
((
B
H
U
C
A.
B.
____
C.
D. none
3. For which situation could you immediately prove
A. I only
____
4. If
B. II only
and
?
C. III only
using the HL Theorem?
D. II and III
, which additional statement does NOT allow you to conclude that
A.
B.
____
C.
D.
5. What other information do you need in order to prove the triangles congruent using the SAS Congruence
Postulate?
A
B
A.
B.
____

D
C.
D.
6. Which overlapping triangles are congruent by ASA?
A.
B.
____
C
C.
D.
7. Supply the missing reasons to complete the proof.
Given:
and
Prove:

N
P
O
M
Q
A. ASA; Substitution
B. SAS; Corresp. parts of
____
C. AAS; Corresp. parts of
D. ASA; Corresp. parts of
8. Find the value of x. The diagram is not to scale.
Given:
,
S
R
A. 19
____
9.
T
U
B. 21
C. 142
is the bisector of
and
is the bisector of
SSS, SAS, or ASA would you use to help you prove
A. AAS
B. SSS
C. SAS
D. 24
. Also,
?
. Which of AAS,
D. ASA
____ 10. Given
A. 13
and
B. 4
____ 11. Given
A. 46
B. 64
, find the length of QS and TV.
C. 14
D. 27
and
, find
C. 47
and
D. 67
____ 12. What is the missing reason in the two-column proof?
Given:
Prove:
bisects
and
bisects
B
<
A
C
>
D
Statements
Reasons
1.
2.
3.
bisects
1. Given
2. Definition of angle bisector
3. Reflexive property
4.
5.
6.
bisects
4. Given
5. Definition of angle bisector
6.
?
A. SAS Postulate
B. ASA Postulate
C. AAS Theorem
D. SSS Postulate
____ 13. Find the value of x. The diagram is not to scale.
|
|
S
(2 x – 50)°
R
(8 x )°
T
A.
____ 14. What common angle do
U
B.
C.
D. none of these
B
C
A
F
G
A.
B.
C.
D.
____ 15. What is the value of x?
|
E
xº
D
113.5°
|
F
Drawing not to scale
A. 56.75°
B. 123.25°
C. 66.5°
D. 33.25°
C. 66°
D. 132°
____ 16. What is the value of x?
48°
21
21
xº
Drawing not to scale
A. 142°
B. 71°
____ 17. Justify the last two steps of the proof.
Given:
and
Prove:
E
F
G
H
Proof:
1.
1. Given
2. Given
3.
4.
2.
3.
4.
A. Symmetric Property of
B. Symmetric Property of
; SAS
; SSS
C. Reflexive Property of
D. Reflexive Property of
; SAS
; SSS
____ 18. R, S, and T are the vertices of one triangle. E, F, and D are the vertices of another triangle.
RS = 4, and EF = 4. Are the two triangles congruent? If yes, explain and
tell which segment is congruent to
A. yes, by ASA;
B. yes, by SAS;
C. yes, by AAS;
D. No, the two triangles are not congruent.
____ 19. What common side do
A
B
C
D
E
F
G
A.
B.
H
C.
D.
____ 20. From the information in the diagram, can you prove
? Explain.
A. yes, by ASA
B. yes, by AAA
C. yes, by SAS
D. no
____ 21. What additional information will allow you to prove the triangles congruent by the HL Theorem?
A
B
|
C
D
A.
B.
|
E
C.
D.
____ 22. Which pair of triangles is congruent by ASA?
A.
C.
B.
D.
____ 23. State whether
and
are congruent. Justify your answer.
5
A.
B.
C.
D.
5
yes, by SSS only
yes, by either SSS or SAS
yes, by SAS only
No; there is not enough information to conclude that the triangles are congruent.
____ 24. Based on the given information, what can you conclude, and why?
Given:
N
P
O
M
Q
A.
B.
by ASA
by ASA
C.
D.
by SAS
by SAS
____ 25. Name the theorem or postulate that lets you immediately conclude
A
B
(
(
D
C
A. SAS
B. ASA
C. AAS
____ 26. Supply the reasons missing from the proof shown below.
Given:
,
Prove:
D. none of these
|
|
(
(
A
B
D
C
A. ASA; Corresp. parts of
B. SAS; Reflexive Property
C. SSS; Reflexive Property
D. SAS; Corresp. parts of
Geometry Ch 4 Post test
Answer Section
1. ANS: B
PTS: 1
DIF: L3
REF: 4-3 Triangle Congruence by ASA and AAS
OBJ: 4-3.1 To prove two triangles congruent using the ASA Postulate and the AAS theorem
NAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e
STA: 4.1.a
TOP: 4-3 Problem 4 Determining Whether Triangles Are Congruent
KEY: ASA | AAS | reasoning
2. ANS: A
PTS: 1
DIF: L2
REF: 4-3 Triangle Congruence by ASA and AAS
OBJ: 4-3.1 To prove two triangles congruent using the ASA Postulate and the AAS theorem
NAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e
STA: 4.1.a
TOP: 4-3 Problem 1 Using ASA
KEY: ASA
3. ANS: C
PTS: 1
DIF: L3
REF: 4-6 Congruence in Right Triangles
OBJ: 4-6.1 To prove right triangles congruent using the hypotenuse-leg theorem
NAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e
STA: 4.1.a
TOP: 4-6 Problem 1 Using the HL Theorem
KEY: hypotenuse | HL Theorem | right triangle | reasoning
4. ANS: B
PTS: 1
DIF: L3
REF: 4-3 Triangle Congruence by ASA and AAS
OBJ: 4-3.1 To prove two triangles congruent using the ASA Postulate and the AAS theorem
NAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e
STA: 4.1.a
TOP: 4-3 Problem 4 Determining Whether Triangles Are Congruent
KEY: ASA | AAS
5. ANS: C
PTS: 1
DIF: L4
REF: 4-2 Triangle Congruence by SSS and SAS
OBJ: 4-2.1 To prove two triangles congruent using the SSS and SAS Postulates
NAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e
STA: 4.1.a
TOP: 4-2 Problem 2 Using SAS
KEY: SAS | reasoning
6. ANS: A
PTS: 1
DIF: L3
REF: 4-7 Congruence in Overlapping Triangles
OBJ: 4-7.1 To identify congruent overlapping triangles
NAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e
STA: 4.1.a
TOP: 4-7 Problem 2 Using Common Parts
KEY: congruent figures | corresponding parts | overlapping triangles | proof
7. ANS: D
PTS: 1
DIF: L3
REF: 4-4 Using Corresponding Parts of Congruent Triangles
OBJ: 4-4.1 To use triangle congruence and corresponding parts of congruent triangles to prove that parts of
two triangles are congruent
NAT: CC G.CO.12| CC G.SRT.5| G.2.e| G.3.e
STA: 4.1.a
TOP: 4-4 Problem 1 Proving Parts of Triangles Congruent
KEY: ASA | corresponding parts | proof | two-column proof
8. ANS: A
PTS: 1
DIF: L4
REF: 4-5 Isosceles and Equilateral Triangles
OBJ: 4-5.1 To use and apply properties of isosceles and equilateral triangles
NAT: CC G.CO.10| CC G.CO.13| CC G.SRT.5| G.1.c| G.2.e| G.3.e
STA: 4.1.a
TOP: 4-5 Problem 2 Using Algebra
KEY: Isosceles Triangle Theorem | isosceles triangle | problem solving | Triangle Angle-Sum Theorem
9. ANS: D
PTS: 1
DIF: L4
REF: 4-7 Congruence in Overlapping Triangles
OBJ: 4-7.2 To prove two triangles congruent using other congruent triangles
10.
11.
12.
13.
14.
15.
16.
17.
18.
NAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e
STA: 4.1.a
TOP: 4-7 Problem 2 Using Common Parts
KEY: corresponding parts | congruent figures | ASA | SAS | AAS | SSS | reasoning
ANS: A
PTS: 1
DIF: L4
REF: 4-1 Congruent Figures
OBJ: 4-1.1 To recognize congruent figures and their corresponding parts
NAT: CC G.SRT.5| G.2.e| G.3.e
STA: 4.1.a
TOP: 4-1 Problem 2 Using Congruent Parts
KEY: congruent polygons | corresponding parts
ANS: A
PTS: 1
DIF: L4
REF: 4-1 Congruent Figures
OBJ: 4-1.1 To recognize congruent figures and their corresponding parts
NAT: CC G.SRT.5| G.2.e| G.3.e
STA: 4.1.a
TOP: 4-1 Problem 2 Using Congruent Parts
KEY: congruent polygons | corresponding parts
ANS: B
PTS: 1
DIF: L3
REF: 4-3 Triangle Congruence by ASA and AAS
OBJ: 4-3.1 To prove two triangles congruent using the ASA Postulate and the AAS theorem
NAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e
STA: 4.1.a
TOP: 4-3 Problem 2 Writing a Proof Using ASA
KEY: ASA | proof | two-column proof
ANS: C
PTS: 1
DIF: L4
REF: 4-5 Isosceles and Equilateral Triangles
OBJ: 4-5.1 To use and apply properties of isosceles and equilateral triangles
NAT: CC G.CO.10| CC G.CO.13| CC G.SRT.5| G.1.c| G.2.e| G.3.e
STA: 4.1.a
TOP: 4-5 Problem 3 Finding Angle Measures
KEY: Isosceles Triangle Theorem | isosceles triangle
ANS: A
PTS: 1
DIF: L2
REF: 4-7 Congruence in Overlapping Triangles
OBJ: 4-7.1 To identify congruent overlapping triangles
NAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e
STA: 4.1.a
TOP: 4-7 Problem 1 Identifying Common Parts
KEY: overlapping triangle | congruent parts
ANS: D
PTS: 1
DIF: L3
REF: 4-5 Isosceles and Equilateral Triangles
OBJ: 4-5.1 To use and apply properties of isosceles and equilateral triangles
NAT: CC G.CO.10| CC G.CO.13| CC G.SRT.5| G.1.c| G.2.e| G.3.e
STA: 4.1.a
TOP: 4-5 Problem 2 Using Algebra
KEY: Isosceles Triangle Theorem | Triangle Angle-Sum Theorem | isosceles triangle
ANS: C
PTS: 1
DIF: L2
REF: 4-5 Isosceles and Equilateral Triangles
OBJ: 4-5.1 To use and apply properties of isosceles and equilateral triangles
NAT: CC G.CO.10| CC G.CO.13| CC G.SRT.5| G.1.c| G.2.e| G.3.e
STA: 4.1.a
TOP: 4-5 Problem 2 Using Algebra
KEY: isosceles triangle | Converse of Isosceles Triangle Theorem | Triangle Angle-Sum Theorem
ANS: D
PTS: 1
DIF: L3
REF: 4-2 Triangle Congruence by SSS and SAS
OBJ: 4-2.1 To prove two triangles congruent using the SSS and SAS Postulates
NAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e
STA: 4.1.a
TOP: 4-2 Problem 1 Using SSS
KEY: SSS | reflexive property | proof
ANS: A
PTS: 1
DIF: L3
REF: 4-4 Using Corresponding Parts of Congruent Triangles
OBJ: 4-4.1 To use triangle congruence and corresponding parts of congruent triangles to prove that parts of
two triangles are congruent
NAT: CC G.CO.12| CC G.SRT.5| G.2.e| G.3.e
STA: 4.1.a
TOP: 4-4 Problem 1 Proving Parts of Triangles Congruent
KEY:
19. ANS:
REF:
OBJ:
STA:
KEY:
20. ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
21. ANS:
OBJ:
NAT:
TOP:
KEY:
22. ANS:
REF:
OBJ:
NAT:
KEY:
23. ANS:
REF:
OBJ:
NAT:
TOP:
24. ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
25. ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
26. ANS:
REF:
OBJ:
NAT:
STA:
KEY:
ASA | corresponding parts | word problem
A
PTS: 1
DIF: L3
4-7 Congruence in Overlapping Triangles
4-7.1 To identify congruent overlapping triangles
NAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e
4.1.a
TOP: 4-7 Problem 1 Identifying Common Parts
overlapping triangle | congruent parts
A
PTS: 1
DIF: L3
4-3 Triangle Congruence by ASA and AAS
4-3.1 To prove two triangles congruent using the ASA Postulate and the AAS theorem
CC G.SRT.5| G.2.e| G.3.e| G.5.e
STA: 4.1.a
4-3 Problem 4 Determining Whether Triangles Are Congruent
ASA | reasoning
C
PTS: 1
DIF: L3
REF: 4-6 Congruence in Right Triangles
4-6.1 To prove right triangles congruent using the hypotenuse-leg theorem
CC G.SRT.5| G.2.e| G.3.e| G.5.e
STA: 4.1.a
4-6 Problem 2 Writing a Proof Using the HL Theorem
hypotenuse | HL Theorem | right triangle | reasoning
B
PTS: 1
DIF: L2
4-3 Triangle Congruence by ASA and AAS
4-3.1 To prove two triangles congruent using the ASA Postulate and the AAS theorem
CC G.SRT.5| G.2.e| G.3.e| G.5.e
STA: 4.1.a
TOP: 4-3 Problem 1 Using ASA
ASA
B
PTS: 1
DIF: L3
4-2 Triangle Congruence by SSS and SAS
4-2.1 To prove two triangles congruent using the SSS and SAS Postulates
CC G.SRT.5| G.2.e| G.3.e| G.5.e
STA: 4.1.a
4-2 Problem 3 Identifying Congruent Triangles
KEY: SSS | SAS | reasoning
A
PTS: 1
DIF: L3
4-3 Triangle Congruence by ASA and AAS
4-3.1 To prove two triangles congruent using the ASA Postulate and the AAS theorem
CC G.SRT.5| G.2.e| G.3.e| G.5.e
STA: 4.1.a
4-3 Problem 4 Determining Whether Triangles Are Congruent
ASA | reasoning
B
PTS: 1
DIF: L2
4-3 Triangle Congruence by ASA and AAS
4-3.1 To prove two triangles congruent using the ASA Postulate and the AAS theorem
CC G.SRT.5| G.2.e| G.3.e| G.5.e
STA: 4.1.a
4-3 Problem 4 Determining Whether Triangles Are Congruent
ASA | AAS | SAS
D
PTS: 1
DIF: L4
4-5 Isosceles and Equilateral Triangles
4-5.1 To use and apply properties of isosceles and equilateral triangles
CC G.CO.10| CC G.CO.13| CC G.SRT.5| G.1.c| G.2.e| G.3.e
4.1.a
TOP: 4-5 Problem 1 Using the Isosceles Triangle Theorems
segment bisector | isosceles triangle | proof | two-column proof