Geometry

Question Analysis

The main focus is to apply the Hinge Theorem to determine a possible length for segment . We have two triangles with congruent side - pairs and different included angles, and we need to use the theorem to find the appropriate range for the length of .

 

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 , .

Since the pairs of corresponding sides in  and

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