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Chapter 5: Relationships Within Triangles 5.5 Inequalities in Triangles Comparison Property of Equality • If a = b + c, and c > 0, then a > b. b a 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. m1 m2 m1 m3 2 3 1 Theorem 5-10 • If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side. B AC BC AB so B A C A C 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? A 27 ft 21 ft C 18 ft B Theorem 5-11 If two angles of a triangle are not congruent, then the larger side lies opposite the larger angle. B B A C so AC BC AB A C Example 3 • List the sides of ΔTUV in order from shortest to longest: T 58 U 62 V Example 3a • List the sides of ΔXYZ in order from shortest to longest. Explain your reasoning! Y 40 X 60 Z 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. Y XZ XY ZY XY YZ XZ XZ YZ XY X Z 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