Geometry

Question Analysis

The main focus is applying the Hinge Theorem to compare the lengths of  and . Given the angles and congruent - side markings in the triangles formed within the figure, we 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, the side opposite the larger included angle is longer.

Step - by - Step Solution

1. Consider  and . The sides  and  is common.

The included angle  and .

Since  >  (  >