Geometry

Question Analysis

The main focus is applying the Hinge Theorem to find the range of possible values of . Given two triangles  and  with congruent - side pairs and different side lengths, we'll set up and solve inequalities based on the theorem.

Key Concept Explanation

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

Step - by - Step Solution

1. In  and

Since  and , and  > , by the Hinge Theorem, =  is greater than  =. So, we set up the inequality  > .

Solve the inequality  > :

Subtract 2 from both sides:

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