£ Chapter: Quadrilaterals
f , ( Lesson: Parallelograms
Properties of Parallelograms Practice
|^ W Complete these problems in your notebook.
Name
KEY_
Use the diagram of the parallelogram to the right to answer the following questions.
1. If m<MPO = 122°, then m<PON = _58_ .
2. If m<PMN = 74°, then m<NOP = _74_ .
3. If m<4 = 36°, then m< _2_
= 36°.
4. If m<MNO = 106° and m<4 = 47°,
thenm<3= 59
3x + 2 = x + 14
5. If NR - 3x + 2 and RP = x + 14, then
x = _6_^ NR = _20_ and NP = _40
2(2x + 4) = 7x - 28
6. If MR = 2x + 4 and MO = 7x - 28, then
x= 12_,RO = 28 and MO = 56
7. If m<PMN = 8x - 5 and m<PON = 4x + 19, then
8x - 5 = 4x + 19
x = _6 , m<PMN = _43°
and m<MNO = _137
.
8. If m<MPO = 9x + 2 and m<PON = 5x + 10, then
x = _12__, m<MPO = _110'_,
m<PON = _7(T
, and m<PMN = _70"
.
(9x + 2) + (5x + 10) = 180
Complete each statement using parallelogram KLMN.
9. IfKN = 3x-5andLM = x + 9,
then KN = _16
,
3x - 5 = x + 9
10. If KL = - and MN = 2x - 9, - = 2x - 9
2
2
thenKL= 3
L
11. If m<L = 4x + 11 and m<K = 6x -1, (4x + 11) + (6x - 1) = 180
then m<K = JLOr
.
12. Ifm<L = x + 40andm<N = 3x-6,
thenm<L= 63
x + 40 = 3 x - 6
Find the values of x. y and z if each quadrilateral is a parallelogram.
13
rv—v\
= _44°
y = _50"
z = 86°
x = 73'
v= 31"
z = 76°
X
15.
116°
x
z
- _64"
y = __116S'
z - 116"
X
V
16. In parallelogram WXYZ, if m<W = 3p and m<X = 4p + 33, find p and the measure of
all four angles, p = 21; 63°, 117°, 63' , 117"
Explain why it is impossible for each figure to be a parallelogram.
17.
NO
18. NO
125°
19. Quad TRAP has vertices T(-2, -1), R(2, 3), A(7, 3), and P(3, -1). Is TRAP also a
parallelogram? Explain why or why not?
Yes. Opposite sides are parallel,
slope TR -1
slope RA = 0
slope AP = 1
slope TP = 0