5.5 Triangle Inequalities
In a scalene triangle the side opposite the
largest angle is the longest side.
A
100
Name the longest side
30
50
B
C
Mar 1­9:38 AM
Ex. 1
A
70
B
50
30
Ex. 2
D
90
60
80
A
C
Name the shortest side
C
Name the
longest side if:
m A= x-30
m B = 2x + 10
B
m C=x
Mar 1­9:42 AM
1
Ex. 3
B
7
√5
A
6 C
Put the angles in
order from least to
greatest
Mar 1­9:47 AM
Triangle Inequality Theorem
The sum of 2 sides of a triangle is greater
than the 3rd side
3
5
6
Mar 1­9:51 AM
2
Ex. 4 Do the following sides form a triangle?
a) 4, 7, 10
b) 4, 6, 8
c) 14, 14, 0.2
d) 5, 5, 15
e) 3, 9, 12
Mar 1­9:53 AM
If given two sides of a triangle and you want
to find the range of the 3rd side
subtract and add the two numbers
Ex. 5
Given sides 3 and 8 find the range of the 3rd
side.
Mar 1­9:57 AM
3
Ex. 6
Find the range of the 3rd side if two sides
are c and d, where c is greater than d
Mar 1­10:01 AM
A
B
D
C
Mar 1­10:04 AM
4