Geometry

Question Analysis

The main focus is applying the Hinge Theorem to determine a possible length for segment . Given the angles and congruent - side markings in the triangles formed within the figure, we need to use the theorem to find the appropriate length range for .

 

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

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