Geometry

Question Analysis

The main focus is using the Triangle Mid - Segments Theorem to determine the value of . We need to identify the mid - segment  and the side  it's parallel to in , and then apply the theorem's relationship to form an equation.

Key Concept Explanation

The Triangle Mid - Segments Theorem states that a mid - segment of a triangle (a line segment connecting the midpoints of two sides of a triangle) is parallel to the third side of the triangle and half its length. Here,  is a mid - segment of .

Step-by-Step Solution

1. Set up the equation based on the theorem:

Since  is the mid - point of  and  is the mid - point of ,  is a mid - segment of . According to the theorem, .

We know that  and . So the equation is

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