Geometry

Question Analysis

The main focus is applying the Triangle Mid - Segments Theorem to determine which segment is parallel to . We need to identify the 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 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: lies on

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