Geometry

Question Analysis

The main focus is to apply the Angle - Side Relationship Theorem to order the sides of  from longest to shortest. This requires identifying the largest and smallest angles and then determining the sides opposite them.

Key Concept Explanation

The Angle - Side Relationship Theorem states that in a triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. This relationship is based on the geometric principle that as the measure of an angle increases, the length of the side opposite to it also increases.

Step - by - Step Solution

1. Identify the angles: In ,  and . Using the angle - sum property of a triangle (), we find .

2. Determine the largest and smallest angles: The angles are

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