Geometry CP - Ch. 4 Review
1. If
A.
, which of the following can you NOT conclude as being true?
B.
C.
D.
2.
A.
B.
3. Given
A. 7
C.
and
D.
, find the length of QS and TV.
C. 8
D. 2
B. 25
4. The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to
scale.
d°
21°
g
13
b
f°
e°
5
A. 5
12
69°
c
B. 21
5. Justify the last two steps of the proof.
Given:
and
Prove:
C. 13
D. 12
R
S
T
U
Proof:
1.
1. Given
2. Given
3.
4.
2.
3.
4.
A. Reflexive Property of ; SAS
B. Symmetric Property of ; SSS
C. Reflexive Property of ; SSS
D. Symmetric Property of ; SAS
6. What other information do you need in order to prove the triangles congruent using the SAS Congruence
Postulate?
(
(
A
B
A.
B.
C
D

7. Which triangles are congruent by ASA?
C.
D.

F
A
(
V
T ))
((
B
(
)
G
H
U
C
A.
B.
C.
D. none
8. Which pair of triangles is congruent by ASA?
A.
C.
B.
9. If
D.
and
?
, which additional statement does NOT allow you to conclude that
A.
B.
C.
D.
10. Can you use the SAS Postulate, the AAS Theorem, or both to prove the triangles congruent?
|
)
|
)
A. SAS only
B. either SAS or AAS
C. AAS only
D. neither
11. What is the value of x?
34°
21
21
xº
Drawing not to scale
A. 156°
B. 146°
C. 73°
12. Supply the missing reasons to complete the proof.
Given:
and
Prove:
D. 78°
S
U
T
R
V
A. ASA; Substitution
B. AAS; Corresp. parts of
C. ASA; Corresp. parts of
D. SAS; Corresp. parts of
13. What is the value of x?
xº
74°
Drawing not to scale
A. 32°
B. 106°
C. 53°
D. 148°
14. Is there enough information to conclude that the two triangles are congruent? If so, what is a correct congruence
statement?
A
|
|
B
A.
B.
C.
D.
C
D
Yes;
.
Yes;
.
Yes;
.
No, the triangles cannot be proven congruent.
15. What additional information will allow you to prove the triangles congruent by the HL Theorem?
A
B
|
C
|
D
E
A.
B.
C.
D.
16. What common side do
A
B
C
D
E
F
G
H
A.
B.
C.
D.
17. What common angle do
C
D
E
F
G
A.
B.
C.
D.
18. Find the value of x. The diagram is not to scale.
|
|
S
(3 x – 50)°
R
(7 x )°
T
U
19. The legs of an isosceles triangle have lengths
of the base?
20. Two sides of an equilateral triangle have lengths
the third side:
or
?
and
and
. The base has length
. What is the length
. Which expression could be the length of
21. Find the value of x. The diagram is not to scale.
Given:
,
S
R
T
U
Geometry CP - Ch. 4 Review
Answer Section
1. ANS:
OBJ:
NAT:
KEY:
2. ANS:
OBJ:
NAT:
KEY:
3. ANS:
OBJ:
NAT:
KEY:
4. ANS:
OBJ:
NAT:
KEY:
5. ANS:
REF:
OBJ:
NAT:
KEY:
6. ANS:
REF:
OBJ:
NAT:
KEY:
7. ANS:
REF:
OBJ:
NAT:
KEY:
8. ANS:
REF:
OBJ:
NAT:
KEY:
9. ANS:
REF:
OBJ:
NAT:
KEY:
10. ANS:
REF:
OBJ:
NAT:
KEY:
A
PTS: 1
DIF: L3
REF: 4-1 Congruent Figures
4-1.1 To recognize congruent figures and their corresponding parts
CC G.SRT.5| G.2.e| G.3.e
TOP: 4-1 Problem 1 Finding Congruent Parts
congruent polygons | corresponding parts | word problem
D
PTS: 1
DIF: L2
REF: 4-1 Congruent Figures
4-1.1 To recognize congruent figures and their corresponding parts
CC G.SRT.5| G.2.e| G.3.e
TOP: 4-1 Problem 1 Finding Congruent Parts
congruent polygons | corresponding parts
A
PTS: 1
DIF: L4
REF: 4-1 Congruent Figures
4-1.1 To recognize congruent figures and their corresponding parts
CC G.SRT.5| G.2.e| G.3.e
TOP: 4-1 Problem 2 Using Congruent Parts
congruent polygons | corresponding parts
A
PTS: 1
DIF: L3
REF: 4-1 Congruent Figures
4-1.1 To recognize congruent figures and their corresponding parts
CC G.SRT.5| G.2.e| G.3.e
TOP: 4-1 Problem 2 Using Congruent Parts
congruent polygons | corresponding parts
C
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
TOP: 4-2 Problem 1 Using SSS
SSS | reflexive property | proof
D
PTS: 1
DIF: L4
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
TOP: 4-2 Problem 2 Using SAS
SAS | reasoning
A
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
TOP: 4-3 Problem 1 Using ASA
ASA
D
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
TOP: 4-3 Problem 1 Using ASA
ASA
B
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
TOP: 4-3 Problem 4 Determining Whether Triangles Are Congruent
ASA | AAS
C
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
TOP: 4-3 Problem 4 Determining Whether Triangles Are Congruent
ASA | AAS | reasoning
11. 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
TOP: 4-5 Problem 2 Using Algebra
KEY: isosceles triangle | Converse of Isosceles Triangle Theorem | Triangle Angle-Sum Theorem
12. ANS: C
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
TOP: 4-4 Problem 1 Proving Parts of Triangles Congruent
KEY: ASA | corresponding parts | proof | two-column proof
13. ANS: A
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
TOP: 4-5 Problem 2 Using Algebra
KEY: isosceles triangle | Isosceles Triangle Theorem | Triangle Angle-Sum Theorem | word problem
14. ANS: B
PTS: 1
DIF: L2
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
TOP: 4-6 Problem 1 Using the HL Theorem
KEY: hypotenuse | HL Theorem | right triangle | reasoning
15. 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
TOP: 4-6 Problem 2 Writing a Proof Using the HL Theorem
KEY: hypotenuse | HL Theorem | right triangle | reasoning
16. ANS: D
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
TOP: 4-7 Problem 1 Identifying Common Parts
KEY: overlapping triangle | congruent parts
17. ANS: C
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
TOP: 4-7 Problem 1 Identifying Common Parts
KEY: overlapping triangle | congruent parts
18. ANS:
PTS:
OBJ:
NAT:
TOP:
KEY:
19. ANS:
11
1
DIF: L4
REF: 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
4-5 Problem 3 Finding Angle Measures
Isosceles Triangle Theorem | isosceles triangle
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
TOP: 4-5 Problem 2 Using Algebra
KEY: isosceles triangle | Isosceles Triangle Theorem | word problem | problem solving
20. ANS:
18 – x only
PTS:
OBJ:
NAT:
TOP:
21. ANS:
14
1
DIF: L4
REF: 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
4-5 Problem 2 Using Algebra
KEY: equilateral triangle | word problem | problem solving
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L4
REF: 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
4-5 Problem 2 Using Algebra
Isosceles Triangle Theorem | isosceles triangle | problem solving | Triangle Angle-Sum Theorem