Download Inequalities Involving Two Triangles

Inequalities Involving Two Triangles
The following two theorems are useful in determining relationships between sides and angles in triangles.
Hinge Thereorm
(SAS Inequality Theorem)
Converse of Hinge
Theorem
(SSS Inequality)
If two sides of one triangle are congruent to two sides of another triangle,
and the included angles are not congruent, then the longer third side is
opposite the larger included angle.
If two sides of one triangle are congruent to two sides of another triangle,
and the third sides are not congruent, then the larger included angle is
opposite the longer third side.
Examples: Refer to each figure to write an inequality relating the given pair of angle or segment measures.
1. 1 ____ 2
2. AD _____ BE
1 2
25
30o
D
9
8
A
U
3. UT ______ TS
12
R
5. 1 ____ 2
12
o
25
35o
50
N
L
12
65o
1
7
65o
2
5
8
S
1
K
6. KPE ____ GPH
16
20
(3x-18)o
20
E
P
12
Write an inequality or pair of inequalities to describe the possible values of x.
7.
8.
5x - 7
5
70o
70o
H
100o 110o
B
6
6
16
28
E
o
P
4. LPM ____ MPN
T
22o
21o
6
50
C
10
12
42o
12
11
6
G
9.
10.
15
40 41
10
71
36 38
12.
14
26
103
50
15
5x-6
11.
3x+14
32
10
5
8
14
250°
65
65
2x+17
(13x-100)°
8
6
13. Find the shortest and longest segment in ∆DEG.
D
50°
14. Find the shortest and longest segment in ∆EFG.
15. Find the shortest and longest segment in the figure.
70°
60°
G
E
60°
40°
80°
F