5 5 Inequalities Involving TWO Triangles What youll

5. 5 Inequalities Involving TWO Triangles What you’ll learn: 1. To apply the SAS Inequality 2. To apply the SSS Inequality

Theorem 5. 13 SAS Inequality/Hinge Theorem If 2 sides of a triangle are congruent to 2 sides of another triangle and the included angle in one triangle has a greater measure than the included angle in the other, then the 3 rd side of the 1 st triangle is longer than the 3 rd side of the 2 nd triangle. B E If AB=DE and AC=DF and A> D, then F BC>EF A C D

Theorem 5. 14 SSS Inequality if 2 sides of a triangle are congruent to 2 sides of another triangle and the 3 rd side in one triangle is longer than the 3 rd side in the other, then the angle between the pair of congruent sides in the 1 st triangle is greater than the corresponding angle in the 2 nd triangle. E A If AB=DE, AC=EF, and D B BC<EF, then A< B C F

Write an inequality relating the given pair of angles or segment measures. 1. 15 20 D A 50 B 15 C P 2. 8 Q S 6 AB _______ CD 4 4 R m PQS ______ m RQS

Write an inequality describe the possible values of x. 1. 3 x-3<33 60 cm 36 cm 33 (3 x-3) 60 cm 30 cm and 3 x-3>0 3 x<36 3 x>3 x<12 x>1 1<x<12 (½x -6) 2. 30 52 30 12 28 ½x-6<52 and ½x-6>0 ½x<58 ½x>6 x<115 x>12 12<x<115

Given: CD AB, m ACB+m BCD<m ABC+m CBD AC=BD Prove: AB<CD 1. CD AB, 1. m ACB+m BCD<m AB C+m CBD AC=BD 2. 2. BC=BC 3. 3. ABC= BCD 4. 4. m ACB+m ABC<m AB 5. C+m CBD 6. 5. m ACB<m CBD 6. AB<CD A C B Given Reflexive Alt. int. angles substitution Subtraction SAS Inequality D

Homework p. 271 10 -20 all, 34 -40 even, skip 38