Geometry

Question Analysis

The main focus is applying the Hinge Theorem to find a possible length for segment . Given the angles and side - length information in the triangles  and , we need to use the theorem to determine 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. In  and , we have ,  (congruent as marked), and  is common.

The included angle ∠URT = 55° and

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