Geometry

Question Analysis

The main focus is applying the Triangle Mid - Segments Theorem to find the length of . We need to identify the mid - points in the triangle and use the relationship between the mid - segment and the side of the triangle.

 

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. Identify the mid - points:

From the markings,  is the mid - point of  and  is a mid - point (implied by the single tick marks on ). So,  is a mid - segment of