Geometry

Question Analysis

The main focus is applying the Hinge Theorem to compare the lengths of  and . Given two triangles with congruent - side pairs and different included angles, we need to use the theorem to determine the relationship between these two sides.

Key Concept Explanation

The Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, but the included angles are different, then the side opposite the larger included angle is longer.

Step - by - Step Solution

1. In , , and in , .

The sides of  and  have congruent markings, indicating two pairs of congruent sides.

Since  >  (  >