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Worksheet 5.6 Hinge Theorem Chapter 5

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Worksheet 5.6 Hinge Theorem Chapter 5
Name ________________________
Refer to each figure given write an inequality relating the given pair of angle or segment measures.
1) mпѓђ1, mпѓђ2
2) mпѓђ1, mпѓђ2
X
F
A
7
G
8
1 2
3) XB, ZB
2
1
24пЃЇ
26пЃЇ
B
5
Y
H
B
5
D
10 C 7
Z
E
4) HJ , KP
5)
P
пЃЇ
L
6)
mпѓђ3, mпѓђ4
5
9
5
85
H
mпѓђ1, mпѓђ2
8
16
3
1 2
8
4
K
16
6
J
G
7) mпѓђPRQ, mпѓђPRS
8) FH , GE
R
7
F
Q
100
30
S
9
5
E
E
G
12
7
9) KP, KG
5
70пЃЇ
12
G
K
87пЃЇ
H
P
P
5
H
Write an inequality or pair of inequalities to describe the possible values of x. Then solve the
inequality to find the values of x.
10)
11)
12)
пЂЁ x пЂ« 5пЂ©
6
12
102пЃЇ
8
7
пЂЁ7 x пЂ« 4 пЂ©пЃЇ
7
пЂЁ3x пЂ­ 2пЂ©
пЂЁ5x пЂ­ 7пЂ©
10
45пЃЇ
95 135
пЂЁ3x пЂ­ 7пЂ©
8
6
8
13)
пЂЁ5x пЂ­ 7пЂ©
пЂЁ5x пЂ­ 7пЂ©
28
пЃЇ
100 110
20
20
пЃЇ
13
14)
15)
65
(2x пЂ« 34)п‚°
38 пЂ­ x
5x пЂ­ 4
20
20
55
18
13
16)
35
пЂЁ 9x
17)
21
пЂ­ 22 пЂ© п‚°
18)
54
48
8
14п‚°
22п‚°
10п‚°
пЂЁ пЂ©
1
41п‚°
7
7
56п‚°
7x пЂ­ 6
13
x п‚°
11x пЂ­ 12
19)
20)
12
(4x пЂ­ 7)п‚°
7
G
21)
5
23
F
35п‚°
21п‚°
7
6
E
4
Factor the following equations.
22) x пЂ­ 2x пЂ­ 15
23) x пЂ­ 23x пЂ« 60
24) x пЂ« 10 x пЂ« 9
25) 4 x пЂ« 8 x пЂ­ 5
26) 4 x пЂ« 7x пЂ« 3
27) 5x пЂ­ 8 x пЂ­ 4
2
2
6
32п‚°
5
3x пЂ« 2
(4 пЂ« 14x )п‚°
2
2
2
2
H
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