1. 5.4 Inequalities in One Triangle

2. Theorem 5.7
If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side. B
3.5 cm
5.5 cm A C
7.5 cm
AB < BC < AC
m<C < m<A < m<B

3. Theorem 5.8
If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.

4. Theorem 5.9 Triangle Inequality
The sum of the lengths of any two sides of a triangle is greater than the length of the third side. B
Example:
cable
Minimum length: =200 ft
Maximum Length : =400 ft A
300 ft
200 < cable < 400
100 ft C