If , then .

If , then .

Section 11.7 : Inequalities in Two Triangles

Learning Targets: Prepares for – G.CO.10

Important Terms and Definitions

The Hinge Theorem (SAS Inequality Theorem): If two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle.

The Converse of Hinge Theorem (SSS Inequality Theorem): If two sides of one triangle are congruent to two sides of another triangle, and the third sides are not congruent, then the larger included angle is opposite the larger third side.

Write an inequality relating the given pair of angles or segment measures.

(ex 1) ,

(ex 2) ,

(ex 3)

(ex 4)

Write an inequality or pair of inequalities to describe the possible values of x. Then solve the inequality to find the possible values of x.

(ex 5)

(ex 6)

(ex 7)

Homework – Section 11.7 : Inequalities in Two Triangles

Write an inequality relating the given pair of angles or segment measures.

1. 2.

3. 4.

Using the figure at the right, complete each blank with a < , >, or =. Explain why.

5. PT _____ QR

6. PT _____ RS

7. ______

Write an inequality or pair of inequalities to describe the possible values of x. Then solve the inequality to find the possible values of x.

8. 9. 10.