Chapter 4 Study Guide
Name: ____________________________
1. Write a equation of a line that passes through point P and is parallel to the line with the
given equation.
a. P(-2, 1), y - 2x = 2
b. P(3, 3), 3y + x = -6
2. Write a equation of a line that passes through point P and is perpendicular to the line
with the given equation.
a. P(4, 3), y - 2x = -3
b. P(-1, -10), 5y + x = 5
3. Know your property of congruence. Give a example of each:
a. Transitive Property; AB  BC , BC  EF , then ____________
b. Symmetric Property;
LM  ______
c. Reflexive Property;
JK  _______
4. Name the intersection of the plane GHT and plane FHT?
5. A triangular bike frame has angles with measures in the ratio 2:1:2. What is the measure
of the smallest angle?
6. Given RED  DOG , what 3 angles are congruent and what 3 segments are congruent?
State the postulate or theorem you would use to prove each pair of triangles congruent. If the
triangles cannot be proved congruent, write not possible.
7.
8.
9.
10.
11.
12.
13.
14.
15.
(16-18) Is it possible to prove LMN  OPQ using the given information? If so, state the
postulate or theorem that you would use (DRAW A PICTURE FOR EACH).
16. L  O , M  P , N  Q
17. LM  OP , MN  PQ , NL  QO
18. L is a right angle, O is a right angle, LM  OP , LN  OQ
19. Find the value of the variable. The diagram is not to scale.
110°
x°
47°
20. The two triangles are congruent. Find the value of the variables. The diagram is not to scale.
d°
30°
g
5
b
f°
4
e°
a°
3
c
QS  10  2v , UV  5v  1, TV  2  2v find the length of QS and TV.
21. Given
(
(
22. Find the values of x and y.
A
y°
|
|
x°
50°
B
D
C
Drawing not to scale
23. What is the measure of a base angle of an isosceles triangle if the vertex angle measures
25° and the two congruent sides each measure 5 units?
24. Find the value of x. The diagram is not to scale.
S
|
(72-x)°
R
|
(10x
)
T
U
DO PROOFS ON A SEPARATE SHEET OF PAPER!!!!!!!
28.
25.
Given: ML PQ , O is the midpoint of MQ
Given:
Prove:
Prove:
LMO  PQO
and
N
P
Q
O
M
R
29. (Hint: use 2 colored pencils to
26.
outline the triangles you are trying to prove
congruent!!)
Given:
MO  QO , N  P
Given:
Prove:
OMQ  OQM
Prove:
,
S
T
R
U
Q
27.
30.
Given:
bisects
and
Prove:
bisects
Given: CA bisects BAD and BCD
Prove:
B
B
<
A
C
>
C
D
A
D