Geometry: Chapter 4 Test Review
PLEASE DO YOUR WORK ON A SEPARATE PIECE OF PAPER!!!!!
Cumulative Review-Chapter 1-3
1. Name the Property of Congruence that justifies the statement:
If ABC  GFH , then GFH  ABC
2. Name the Property of Equality that justifies the statement:
If BC  8 and AC = BC, then AC = 8.
3. Are the lines parallel, perpendicular, or neither?
Line 1: -9x + 3y = 12
Line 2: 2x + 6y = -12
4. Write an equation for the line, in point-slope form, perpendicular to y + 2x = -8 that contains (4, 4).
5. M(6, -8) is the midpoint of
The coordinates of S are (-2, 3). What are the coordinates of R?
6. Find the distance between points P(-2, 8) and Q(5, 12) and simplify the square root.
7. Find the coordinates of the midpoint of the segment whose endpoints are H(2, 5) and K(-8, 11).
Review-Chapter 4
8. If
, then is ONM  PQR ?
9. Use the information given in the diagram. Tell why
A
and
B
D
C
10. Given
and
, find
and
11. What other information do you need in order to prove the triangles congruent using the SAS Congruence
Postulate?
A
B
C
D
12. State whether
and
7
are congruent. Justify your answer.
7
13. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA?
a.
c.
b.
d.
14. Write a two-column proof for the following.
Given:
Prove:
bisects
and
B
<
A
C
D
>
bisects
15. Can you use the ASA Postulate, the AAS Theorem, or both to prove the triangles congruent?
16. What else must you know to prove the triangles congruent by ASA? By SAS?
B
(
A
(
C
D
17. Based on the given information, what can you conclude, and why?
Given:
I
K
J
H
L
19. Complete a two column proof for the following.
Given:
and
Prove:
Q
S
R
P
T
20. In an A-frame house, the two congruent sides extend from the ground to form a 34° angle at the peak. What
angle does each side form with the ground? (HINT: Draw a picture!!)
21. Use the information in the figure. Find
|
E
|
D
116°
F
Drawing not to scale
22. Find the value of x. The diagram is not to scale.
mSRT  7 x  54 ,
Given:
S
R
T
U
23. Write a two-column proof to show that
Given:
and
N
P
Q
O
M
R
24.Write a two-column proof.
Given:
Prove:
,
S
T
R
U
Q
25. The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to
scale.
d°
38°
g
5
b
f°
e°
4
52°
3
26. Given
and
27. Find the values of x and y.
(
(
A
|
|
y°
x°
B
c
47°
D
C
Drawing not to scale
28. Write a two-column proof:
, find the length of QS and TV.
Given: CA bisects BAD and BCD
Prove:
B
C
A
D