Question

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

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 mid - segments

In triangle \(ZXY\), \(R\) is the midpoint of \(ZX\) (since \(ZR = RX\)), \(Q\) is the midpoint of \(ZY\) (since \(ZQ=QY\)), and \(S\) is the midpoint of \(XY\) (since \(XS = SY\)).
The segment \(QR\) is a mid - segment. By the mid - segment theorem, the segment parallel to \(\overline{QR}\) is \(\overline{XS}\) (or \(\overline{SY}\), but since we are looking for a single segment, and considering the triangle structure, if we consider the sub - triangle formed, in the figure, the segment parallel to \(\overline{QR}\) is \(\overline{SY}\) (because \(QR\) connects the mid - points of \(ZX\) and \(ZY\), and \(SY\) is the non - adjacent side relative to the mid - segment \(QR\) in the relevant sub - structure. Another way: If we consider the fact that in a triangle, mid - segments are parallel to the non - adjacent sides.

Answer:

\(\overline{SY}\)