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Inequalities In One Triangle Chapter 5 Section 6 Objective Students will use inequalities involving angles and sides of triangles. Angles and Sides Angles and sides of a triangle have special relationships that involve inequalities. Comparison Property of Inequality If a = b + c and c > 0, then a > b Note: a, b, and c are sides of a triangle. 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. On page 325… Look at Problem 1 Try the “Got It” problem for Problem 1. Theorem 5-10 If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side. Theorem 5-11 If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle. Theorem 5-12 The sum of the lengths of any two sides of a triangle is greater than the length of the third side Y XY + YZ > XZ YZ + XZ > XY XZ + XY >YZ X Z Turn to page 327… Look at Problem 4 at the bottom of the page Try the “Got It” problem #4 On page 328… Try problems #1-8 on your own. In small work groups… Complete problems #9-32 on page 329. Exit Slip 1. Given only 3 measurements, how can you determine if the shape is a triangle? 2. Given three angle measures, how can you determine which side is the shortest? The longest?