Chapter 5: Relationships Within Triangles 5.5 Inequalities in Triangles

Comparison Property of Equality If a = b + c, and c > 0, then a > b. a b c

Corollary Corollary to the Triangle Exterior Angle Theorem: –The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.

Theorem 5-10 If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.

Example 2 A landscape architect is designing a triangular deck. She wants to place benches in the two larger corners. Which corners have the larger angles?

Theorem 5-11 If two angles of a triangle are not congruent, then the larger side lies opposite the larger angle.

Example 3 List the sides of ΔTUV in order from shortest to longest:

Example 3a List the sides of ΔXYZ in order from shortest to longest. Explain your reasoning!

Theorem 5-12 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 4 Can a triangle have sides with the given lengths? 3 ft, 7 ft, 8 ft 3 cm, 6 cm, 10 cm

Example 5 A triangle has sides of lengths 8 cm and 10 cm. Describe the lengths possible for the third side.

Example 5a A triangle has sides of lengths 3 in and 12 in. Describe the lengths possible for the third side.

Homework P. 292: 2-26 EVEN