Geometry

Question Analysis

The main focus is using the Triangle Mid - Segments Theorem to find the length of given that is the mid - point of and is the mid - point of , and the length of the mid - segment .

Key Concept Explanation

The Triangle Mid - Segments Theorem states that a mid - segment of a triangle (a line segment that connects 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. Recall the relationship from the theorem:

Since is the mid - point of and is the mid - point of , is a mid - segment of . According to the Triangle Mid - Segments Theorem,

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