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Chapter 5 Section 5
The Triangle Inequality
The Triangle Inequality

The sum of any two sides of a triangle
must be greater than the third side for
a triangle to exist.
Which of these triangles
actually exist?
18
7
21
45
18
11
18
21
52
18
45
52
21
45
52
What is the length of the third
side,if the triangle is to exist?
17 + 26 > n
n < 42
17 + n > 26
n>9
n
17
26
Opposite the largest side is
the largest angle.

Opposite the smallest side is the
smallest angle. (and vice-versa)
A
T
C
Opposite the largest angle is
the largest side.
List the angles from largest to
smallest
D
8
15
C
12
16
A
10
B



Which side of ∆ RTU is the longest? TU
Name the side of ∆ UST that is the
longest. TS
Which side is greater RS or TS if TU is
an angle bisector? TS
T
30°
80°
R
70° 110°
U
S
List the sides from smallest to
largest.

In ∆ ABC ; m∠A = 3x+20 ,
m∠B=2x+37, m∠C=4x+15.
m ∠ A + m ∠ B + m ∠ C= 180
(3x + 20) + (2x+37) + (4x+15) = 180
9x + 72 = 180
- 72
-72
9x = 108
x=12
m∠A=56 m∠B=61 m∠C=63
BC , AC , AB