Geometry

Question Analysis

The main focus is applying the Triangle Mid - Segments Theorem to determine the length of  using the given information about mid - points  and  and the length of mid - segment .

 

Key Concept Explanation

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

 

Step-by-Step Solution

1. Recall the theorem's relationship:

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

2. Solve for

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