Question

name the segment that is parallel to the given segment.
fg
fg

Explanation:

Step1: Recall the mid - segment theorem

The mid - segment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side.

Step2: Identify the mid - segments

In triangle \(XYZ\), \(F\) is the midpoint of \(XZ\) (since \(XF = FZ\)), \(G\) is the midpoint of \(XY\) (since \(XG=GY\)). The segment \(FG\) is connecting the midpoints of \(XZ\) and \(XY\).

Step3: Determine the parallel segment

By the mid - segment theorem, the segment \(FG\) is parallel to \(ZY\).

Answer:

\(\overline{ZY}\)