b
Geometry: Chapter 4 Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. If
a.
, which of the following can you NOT conclude as being true?
b.
c.
d.
____
2. Name the angle included by the sides
N
and
M
P
a.
b.
c.
d. none of these
____
3. Write an equation for the line perpendicular to y = 7x + 2 that contains (10, 3).
a. y – 3 = 7(x – 10)
c. x – 3 = 7(y – 10)
b.
d.
1
1
y – 3 =  (x – 10)
y – 10 =  (x – 3)
7
7
____
4. 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.
5. Name the Property of Congruence that justifies the statement:
If
.
a. Transitive Property
c. Reflexive Property
b. Symmetric Property
d. none of these
____
6. For which situation could you prove
a. I only
____
b. II only
d. II and III
? Explain.
c. yes, by SAS
d. no
8. Which two lines are parallel?
I.
II.
III.
a. II and III
b. I and III
____
c. III only
7. From the information in the diagram, can you prove
a. yes, by ASA
b. yes, by AAA
____
using the HL Theorem?
c. I and II
d. No, two of the lines are parallel.
9. Name the Property of Congruence that justifies the statement:
If
.
a. Symmetric Property
c. Reflexive Property
b. Transitive Property
d. none of these
10. The two triangles are congruent as suggested by their appearance. Find the value of b, c, d, e, f, and g. The
diagrams are not to scale.
d°
26°
g
13
b
f°
e°
12
64°
5
c
11. Find the value of x. The diagram is not to scale.
|
|
S
(5 x – 60)°
R
(5 x )°
T
U
12. Find the coordinates of the midpoint of the segment whose endpoints are H(2, 13) and K(10, 11).
13.
14. If BCDE is congruent to OPQR, then
is congruent to
15. What is the measure of a base angle of an isosceles triangle if the vertex angle measures 32° and the two
congruent sides each measure 21 units?
32°
21
21
Drawing not to scale
16. Find the value of the variable. The diagram is not to scale.
110°
x°
17. Given
and
18. Find the values of x and y.
(
(
A
|
|
y°
x°
B
47°
62°
D
C
Drawing not to scale
, find the length of QS and TV.
19. M(5, 3) is the midpoint of
The coordinates of S are (7, 4). What are the coordinates of R?
20. Find the distance between points P(1, 4) and Q(3, 8).
21. Write a two-column proof:
Given: BA // DE , C is the midpoint of AD
Prove: BC  CE
B
D
C
A
E
Statements
Reasons
22. Write a two-column proof.
Given:
and
Prove:
Statements
Reasons
Statements
Reasons
B
D
C
A
E
23.
Complete the proof
Given:
Prove:
,
C
D
B
E
A