Lesson 6.2

Name
Class
6-2
Date
Practice
Form K
Properties of Parallelograms
Find the value of x in each parallelogram.
1.
129
x
51
To start, identify the relationship between the
marked angles in the diagram.
The marked angles are consecutive angles. By
Theorem 6-4, the angles are supplementary.
u 1 51 5 180
Then write an equation: x
2.
76
104
26
3.
x
98
4.
154
x
x
82
Algebra Find the values of the variables in $DEFG.
D
E
5. DG 5 2x 1 2, EF 5 3x 2 3, DE 5 3x 1 1, GF 5 2x 1 6 5
6. DG 5 4a, EF 5 5a 2 6, DE 5 3a 1 2, GF 5 2a 1 8 6
G
F
7. DG 5 2r 1 3, EF 5 3r 2 3, DE 5 2r 1 6, GF 5 4r 2 6 6
8. DG 5 2t 2 10, EF 5 t 1 5, DE 5 t 1 15, GF 5 2t 15
Algebra Find the value of b in each parallelogram. Then find each side length
or angle measure.
9.
6; 20.5; 11.7 10.
b 14.5
15; 55; 125
(8s 5)
3b 6.3
(3s 10)
20.5
11. Developing Proof Complete this two-column proof.
V
U
Given: ~QRST , ~TSVU
S
Prove: RQ > VU
Reasons
R
T
Q
Statements
1) ~QRST , ~TSVU
1) 9 Given
2) RQ > ST , 9 ST O VU
2) Theorem 6-3 Opposite sides of ~
3) RQ > VU
3) 9 Trans. Prop. of O
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Name
Class
Date
Practice (continued)
6-2
Form K
Properties of Parallelograms
Algebra Find the value of each variable in each parallelogram.
12.
5
2h
2h 2
13.
h5
14.
2d 1
11
2j 3
2
d3
3d
6
15.
5r
2j 3
4j 19
5r 2
4r 4
In the figure, GH 5 HI 5 IJ . Find each length.
16. EB 5
17. BD 10
18. AF 6.5
19. AK 19.5
20. CD 5
21. GJ 17.25
G
E
A
B
F
5.75
C 5
H
I
J
D
6.5
K
Find the value of a in each parallelogram.
22.
114
38
23.
11a
10
24.
15
(3a 5)
40
3a
110
25. The length of one side of a parallelogram is 3 more than twice the length of the
adjacent side. The perimeter of the parallelogram is 30 cm. Find the lengths of
the two adjacent sides of the parallelogram. 4 cm and 11 cm
26. Reasoning A classmate draws a parallelogram for which one side is twice
as long as the other. If one side is 26 units, what are all the possible
lengths of the perimeter? 78 units or 156 units
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