1. Chapter 5: Relationships Within Triangles 5.5 Inequalities in Triangles

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

3. 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.

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

5. 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?

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

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

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

9. 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.

10. Example 4 Can a triangle have sides with the given lengths? 3 ft, 7 ft, 8 ft 3 cm, 6 cm, 10 cm

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

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

13. Homework P. 292: 2-26 EVEN