Download Chapter 4 Practice Test Geometry Multiple Choice Identify the

Chapter 4 Practice Test Geometry
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Use the information given in the diagram. Tell why
A
B
D
a.
b.
c.
d.
____
C
Reflexive Property, Given
Transitive Property, Reflexive Property
Given, Reflexive Property
Reflexive Property, Transitive Property
2.
a.
____
b.
c.
d°
g
5
b
f°
e°
4
52°
3
a. 4
____
d.
3. The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to
scale.
38°
____
and
4. Given
a. 2
5. Given
a. 22
c
b. 5
c. 3
and
, find the length of QS and TV.
c. 8
d. 20
b. 9
and
b. 11
d. 38
, find
c. 10
and
d. 25
____
6. Justify the last two steps of the proof.
Given:
and
Prove:
R
S
T
U
Proof:
1.
1. Given
2. Given
3.
4.
2.
3.
4.
a. Symmetric Property of ; SSS
b. Reflexive Property of ; SAS
____
7. State whether
and
are congruent. Justify your answer.
7
a.
b.
c.
d.
____
c. Reflexive Property of ; SSS
d. Symmetric Property of ; SAS
7
yes, by either SSS or SAS
yes, by SSS only
yes, by SAS only
No; there is not enough information to conclude that the triangles are congruent.
8. Name the angle included by the sides
N
and
M
P
a.
b.
c.
d. none of these
____
9. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA?
a.
c.
b.
d.
____ 10. From the information in the diagram, can you prove
a. yes, by ASA
b. yes, by AAA
? Explain.
c. yes, by SAS
d. no
____ 11. Can you use the ASA Postulate, the AAS Theorem, or both to prove the triangles congruent?
a. either ASA or AAS
b. ASA only
c. AAS only
d. Neither
____ 12. Based on the given information, what can you conclude, and why?
Given:
I
K
J
H
L
a.
b.
by ASA
by SAS
c.
d.
by ASA
by SAS
____ 13. Name the theorem or postulate that lets you immediately conclude
|
A
D
|
B
C
a. SAS
b. ASA
c. AAS
____ 14. Supply the missing reasons to complete the proof.
Given:
and
Prove:
Q
S
R
P
a. ASA; Substitution
b. SAS; CPCTC
T
c. AAS; CPCTC
d. ASA; CPCTC
d. none of these
____ 15. Find the values of x and y.
(
(
A
|
|
y°
x°
B
47°
D
C
Drawing not to scale
a.
b.
c.
d.
____ 16. What is the measure of a base angle of an isosceles triangle if the vertex angle measures 38° and the two
congruent sides each measure 21 units?
38°
21
21
Drawing not to scale
a. 71°
b. 142°
c. 152°
d. 76°
____ 17. What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 42°?
a. 69°
b. 84°
c. 138°
d. 96°
____ 18. Use the information in the figure. Find
|
E
D
|
116°
F
Drawing not to scale
a. 32°
b. 122°
____ 19. Find the value of x. The diagram is not to scale.
c. 64°
d. 58°
|
|
S
(3 x – 50)°
(7 x )°
R
T
a.
U
b.
c.
d. none of these
c. 16
d. 19
____ 20. Find the value of x. The diagram is not to scale.
Given:
,
S
R
U
T
a. 14
b. 152
____ 21. The sides of an isosceles triangle have lengths
,
. The base has length
of the base?
a. 18
c. 12
b. 4
d. cannot be determined
Short Answer
22.
. List the six pairs of congruent corresponding parts.
Q
P
S
R
T
23. Based on the given information, can you conclude that
Given:
,
, and
? Explain.
. What is the length
24. Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to complete a proof.
Given:
Prove:
B
C
A
D
25. Is
by HL? If so, name the legs that allow the use of HL.
P
Q
S
R
26. Write the missing reasons to complete the flow proof.
Given:
Prove:
are right angles,
B
(
)
A
D
C
27.Can you conclude the triangles are congruent? Justify your answer.
28. Complete the proof by providing the missing reasons.
Given:
Prove:
,
C
D
B
E
A
Statement
1.
2.
3.
4.
5.
,
, and
are right angles
Essay
29. Write a two-column proof.
Given:
and
Prove:
B
D
C
A
E
Reason
1. Given
2. Definition of perpendicular segments
3. ?
4. ?
5. ?
30. Write a two-column proof:
Given:
Prove:
B
C
A
D
Other
31. Is there enough information to prove the two triangles congruent by AAS? If yes, write the congruence
statement and explain. If no, write not possible and tell what other information you would need.
(
Given:
A
B
C
(
D
Chapter 4 Practice Test Geometry
Answer Section
MULTIPLE CHOICE (2 points each question)
1. ANS: A
REF: 4-1 Congruent Figures
2. ANS: D
REF: 4-1 Congruent Figures
3. ANS: C
REF: 4-1 Congruent Figures
4. ANS: C
REF: 4-1 Congruent Figures
5. ANS: C
REF: 4-1 Congruent Figures
6. ANS: C
REF: 4-2 Triangle Congruence by SSS and SAS
7. ANS: A
REF: 4-2 Triangle Congruence by SSS and SAS
8. ANS: A
REF: 4-2 Triangle Congruence by SSS and SAS
9. ANS: B
REF:
4-3 Triangle Congruence by ASA and AAS
10. ANS: A
REF: 4-3 Triangle Congruence by ASA and AAS
11. ANS: A
REF: 4-3 Triangle Congruence by ASA and AAS
12. ANS: A
REF: 4-3 Triangle Congruence by ASA and AAS
13. ANS: A
REF: 4-3 Triangle Congruence by ASA and AAS
14. ANS: D
REF: 4-4 Using Congruent Triangles: CPCTC
15. ANS: D
REF: 4-5 Isosceles and Equilateral Triangles
16. ANS: A
REF: 4-5 Isosceles and Equilateral Triangles
17.ANS:
D
REF: 4-5 Isosceles and Equilateral Triangles
18. ANS: A
REF: 4-5 Isosceles and Equilateral Triangles
TOP: 4-5 Example 2
19. ANS: A
REF: 4-5 Isosceles and Equilateral Triangles
TOP: 4-5 Example 2
20. ANS: A
REF: 4-5 Isosceles and Equilateral Triangles
TOP: 4-5 Example 2
21. ANS: A
REF: 4-5 Isosceles and Equilateral Triangles
SHORT ANSWER ( 10 points each problem)
22. ANS:
Sides:
Angles:
,
,
,
,
REF: 4-1 Congruent Figures
TOP: 4-1 Example 1
23. ANS:
Answers may vary. Sample: Two pairs of sides are congruent, but the angle is not included. There is no SSA
Congruence Theorem, so you cannot conclude
with the information given.
REF: 4-2 Triangle Congruence by SSS and SAS
24. ANS:
Answers may vary. Sample: Since the two triangles share the side
by CPCTC.
REF: 4-4 Using Congruent Triangles: CPCTC
25. ANS:
Yes,
, they are congruent by SAS. Then
TOP:4-4 Example 2
(in each triangle)
REF: 4-6 Congruence in Right Triangles TOP: 4-6 Example 1
26. ANS:
a. Definition of right triangles
b. Converse of Isosceles Triangle Theorem
c. Reflexive property
d. Angle-Angle-Side Congruence Theorem
REF: 4-6 Congruence in Right Triangles TOP: 4-6 Example 2
27. ANS:
Yes, the diagonal segment is congruent to itself, so the triangles are congruent by SAS.
REF: 4-1 Congruent Figures
TOP: 4-1 Example 3
28. ANS:
Step 3: All right angles are congruent.
Step 4: Reflexive Property
Step 5. HL Theorem
REF: 4-7 Using Corresponding Parts of Congruent Triangles
TOP: 4-7 Example 2
ESSAY ( 10 points each problem)
29. ANS:
[4]
Statement
and
1.
2.
3.
4.
[3]
[2]
[1]
Reason
1. Given
2. Vertical angles are congruent.
3. SAS
4. CPCTC
correct idea, some details inaccurate
correct idea, not well organized
correct idea, one or more significant steps omitted
REF: 4-4 Using Congruent Triangles: CPCTC
30. ANS:
[4]
Statement
1.
Reason
and
2.
3.
4.
[3]
[2]
[1]
1. Given
2. Reflexive Property
3. ASA
4. CPCTC
correct idea, some details inaccurate
correct idea, not well organized
correct idea, one or more significant steps omitted
REF: 4-4 Using Congruent Triangles: CPCTC
OTHER ( 10 points each problem)
31. ANS:
Not possible; you have one pair of congruent angles
and one pair of congruent sides
, but you would need to know that one more pair of angles are congruent, either
or
, to prove the triangles congruent by AAS.
REF: 4-3 Triangle Congruence by ASA and AAS
TOP: 4-3 Example 3