Geometry

Question Analysis

The main focus is using the Triangle Mid - Segments Theorem to determine the length of  given that  is the mid - point of  and  is the mid - point of , along with the length of the 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 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. Identify the mid - segment relationship:

Since  is the mid - point of  and  is the mid - point of , by the Triangle Mid - Segments Theorem,  is parallel to  and .

2. Solve for

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