5-2 Inequalities and Triangles

Exterior Angle Inequality Theorem The measure of the exterior angle of a triangle is greater than either of its remote interior angles 2 1 3 4

Examples: Which angle has the greatest measure? 1. 2. 5 4 5 4 1 2 3 1 2 3 a.) <1, <2, <3 b.) <2, <3, <5 c.) <1, <2, <3, <4, <5

Theorem 5.9 In a triangle, the larger angle (longer side) is opposite the longer side (larger angle) B S 65 4.8 3.6 40 75 C A U V 5.1 Since <C is larger, ____ is the longest side and ____ is the shortest side Since US is the shortest side, <______ is the smallest angle and <______ is the largest angle

Example: Determine the relationship between each. Write <,> or = <WXY____<XYW <XZY_____<XYZ <WYX____<XWY 12 X W 18 15 14 Y Z 17

Example: List the sides of triangle MNO in order, longest to shortest if m<M=4x+20, m<N=3x+10 and m<O=3x-20 List angles of triangle KLM in order from least to greatest if KL=x-4, LM=x+4 and KM=2x-1 and the perimeter of the triangle is 27