5.6: Inequalities in 2 Triangles Use the Hinge Theorem & its converse to find a range of values for a given side or angle. Think About It! The angle that a person makes as he or she is sitting changes with the task. The diagram shows the position of a student as his desk. In which position is the angle measure at which he is sitting the greatest? The least? Justify your answer. Theorem Hypothesis Conclusion Hinge Theorem: If 2 sides of one triangle are congruent to 2 sides of another triangle and the included angles are not congruent, then the longer 3 rd side is across from the _________________ included angle. Converse of the Hinge Theorem If 2 sides of one triangle are congruent to 2 sides of another triangle and the third sides are not congruent, then the larger 3 rd angle is across from the _________________________ included side. Directions: Write an inequality to compare the given measures Example 1: SR and PQ Example 2: mG and mL