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Triangle Inequalities
Objective
• I CAN discover the Triangle Inequality
Theorem and apply inequalities in one
triangle.
The DHS
Chick-Fil-A Run
x
The DHS Football team is headed to M&T
Bank stadium for the state playoffs. The
game isn’t until 7 PM, so they decide to
stop for Chick-Fil-A on the way there. A few
players don’t want to stop, and head
straight for the stadium. Which of the
following is a possible distance from DHS to
M&T Bank Stadium?
25
6
12
18
20
16
Triangle Sides
• If one side of a triangle is longer than another side,
then the angle opposite the longer side has a greater
measure than the angle opposite the shorter side.
B
5
9
C
A
7
Examples
• List the Angles from largest to smallest
Largest P
Largest C
Medium M
Medium B
Smallest N
Smallest A
Triangle Angles
• If one angle of a triangle has a greater
measure than another angle, then the side
opposite the greater angle is longer than the
side opposite the lesser angle.
E
77°
65°
D
38°
F
Examples
• List the sides of triangle from largest to
smallest
Largest QS
Largest CB
Medium QR
Medium CA
Smallest RS
Smallest AB
Triangle Inequality Theorem
• The sum of the lengths of any two sides of a
triangle is greater than the length of the third
side.
Example
• Do these numbers represent a triangle?
1.) 9, 7, 12
2.) 5, 5, 10
3.) 1, 4, 6
4.) 6, 6, 2
Finding Range of Third Side
• If you are given two sides of a triangle you can
determine the range that the third side must
fall in.