1. Triangle Inequalities

2. Definitions Theorem 5-12 Triangle inequality Theorem- Sum of the lengths of any two sides of a triangle is greater than the length of the third side.

3. Example: If the lengths of two sides of a triangle are ten centimeters and fifteen centimeters, between what two numbers must the measure of the third side fall? let t = the length of the third side of the triangle By the Triangle Inequality Theorem, each of these inequalities must be true 10+15 >t 15+t>10 10+t>15 (see example 25>t t>-5 t>5 2 page 268) The lengths of the third side must fall in the range included in all three inequalities