Geometry

Question Analysis

The main focus is using the Triangle Mid - Segments Theorem to find the value of . Given the lengths of the mid - segment and the side it's parallel to, we'll 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

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