Geometry

Question Analysis

The main focus is applying the Triangle Mid - Segments Theorem to determine the value of . Given the lengths of the mid - segment  and the side  it's parallel to, we'll use the theorem's relationship to create 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

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