Chapter 5.5 Inequalities in Triangles

Property: Comparison Property of Inequality If a = b+c and c > 0, then a > b Proof of the comparison property – Given: a = b + c, c > 0 – Prove: a > b StatementsReasons 1.c > 0 2.b + c > b b + c > b 4.a = b + c 5.a > b 1.Given 2.Addition Property of Inequality 3.Simplify 4.Given 5.Substitute a for b + c in Statement 3

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 and

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

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

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. Z Y X

Classwork/Homework Pgs 293 #4-27