Inequalities in One Triangle Section 5-5 Inequalities in One Triangle

Theorem 5-10 Longest sideLargest angle Shortest side Smallest angle

Example: N D A 6 8 10

Theorem 5-11 (Converse) Largest angleLongest side Smallest angleShortest side

Example: C A T CT < TA < CA

Shortest Side: _________. Shortest Side: _________ Shortest Side: _________ Shortest Side: _________ Shortest Side: _________ Largest Side: _________ Largest Side: _________ Largest Side: _________

Smallest Angle: _________. Smallest Angle: _________ Smallest Angle: _________ Smallest Angle: _________ Smallest Angle: _________ Largest Angle: _________ Largest Angle: _________ Largest Angle: _________

List the sides from least to greatest PN, PO, ON, NM, MO 55° 50° 75° P 55° 87° 38° N M

RECALL Exterior Angle Theorem B C 1

Exterior Angle Inequality Theorem The measure of an exterior Angle is always greater than the measure of a non-adjacent angle

A B C 1

Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Side + Side > Largest Side

Example #1: Is it possible for a triangle to have sides with the lengths as indicated? a.) 6, 6, 5 b.) 3, 4, 8 c.) 2.5, 4.1, 5.0 Yes No Yes

Practice Problems 5in, 2in, 8in. 6m, 12m, 15m 3ft, 2ft, 3 ft 50cm, 60cm, 111cm 1in, 1in, 2in

The lengths of two sides of a triangle are 8 and 10 The lengths of two sides of a triangle are 8 and 10. Then, the length of the third side must be greater than ______ but less than ______. 2 18 2<x<18

Practice Problems 7 and 12 7 and 8 9 and 15 12 and 13 5 and 5 Find possible measures for the 3rd segment of the triangle given side lengths: 7 and 12 7 and 8 9 and 15 12 and 13 5 and 5

More practice problems!! Solve the inequality AB+AC>BC A x + 2 + x + 3 > 3x – 2 2x + 5 > 3x – 2 7 > x x < 7 x + 2 x + 3 C B 3x - 2