Geometry

Question Analysis

The main focus is applying the Triangle Mid - Segments Theorem to determine which of the given segments is parallel to . We need to identify mid - points of the triangle's sides and the corresponding mid - segments.

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) is parallel to the third side of the triangle and half of its length.

Step-by-Step Solution

1. Identify the mid - points:

From the markings,  is the mid - point of  and  is the mid - point of . So,  is a mid - segment of .

The side of  that  is parallel to is the side it does not intersect, which is .

Option Analysis

A.Segment XY: Since