If line PQ ∥ line m, then line segment PQ ∥ line m.
Meaning of parallel: Two lines are parallel if they are in the same plane and never meet.
Line vs segment: A line segment is just a part of a line.
Every point of the segment lies on its line.
In symbols:
\(\overline{PQ}\) is a part of line \(PQ\).
So, \(\overline{PQ} \subset PQ\).
Given: line \(PQ\) is parallel to line \(m\).
Write it in symbols:
\(PQ \parallel m\).
Since every point of \(\overline{PQ}\) lies on \(PQ\),
and \(PQ\) is parallel to \(m\),
the segment cannot meet \(m\) either.
Therefore, \(\overline{PQ} \parallel m\).
So the statement is True.