Geometry

Question Analysis

The main focus is applying the Hinge Theorem to compare the measures of  and . Given the side lengths of  and , we use the theorem to establish the relationship between these two angles.

Key Concept Explanation

The Hinge Theorem: If two sides of one triangle are congruent to two sides of another triangle, but the third sides are different, the larger included angle is opposite the longer third side.

Step - by - Step Solution

1. In  and ,  and  is common.

The side  and .

Since >  (  > ), by the Hinge Theorem, the angle opposite  (which is ) is larger than the angle opposite