Inequalities for Two Triangles Section 6-5 Inequalities for Two Triangles

Theorem 6-5: SAS Inequality Thm. If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.

The SAS Inequality Theorem is also referred to as the “Hinge Theorem”

Example #1: therefore… B A C E D F

Example #2: What can you deduce? Given: N is the midpoint of ; I A T N 1 What can you deduce?

Theorem 6-6: SSS Inequality Thm. If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second triangle.

Example: B A C therefore… E D F