Question

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

Explanation:

Step1: Recall the mid - segment theorem

In a triangle, the mid - segment (a segment connecting the mid - points of two sides of a triangle) is parallel to the third side.

Step2: Analyze the given triangle

In \(\triangle MON\), \(R\) is the mid - point of \(MO\) (since \(MR = RO\) as indicated by the tick marks), \(Q\) is the mid - point of \(ON\) (since \(OQ=QN\) as indicated by the tick marks). The segment \(RQ\) is a mid - segment. Also, \(S\) is the mid - point of \(MN\) (since \(MS = SN\) as indicated by the tick marks). The segment \(QS\) is part of the figure.
We know that in a triangle, if we consider the mid - segments. The segment \(RQ\) is parallel to \(MN\), but we are looking at the relationship for \(QS\).
Since \(R\) is the mid - point of \(MO\) and \(S\) is the mid - point of \(MN\), by the mid - segment theorem of a triangle (a segment joining the mid - points of two sides of a triangle is parallel to the third side), the segment \(RS\) is parallel to \(ON\).
Now, for the segment \(QS\), since \(Q\) is the mid - point of \(ON\) and \(S\) is the mid - point of \(MN\), by the mid - segment theorem of a triangle, the segment \(QS\) is parallel to \(MO\).

Answer:

\(\overline{MO}\)