Answer:
not necessarily
Explanation:
You want to know if two lines are parallel if they are perpendicular to the same line.
Plane
If the two lines of interest are distinct (not coincident), and all of the lines lie in the same plane, then ...
yes, two lines perpendicular to the same line are parallel
3-space
If the lines are not confined to a plane, the two lines of interest may be skew with respect to each other, or they may intersect with the "transversal" at a point.
For example, the x- and y-axes are both perpendicular to the z-axis, but are not parallel.
no, two lines not in the same plane with the "transversal" may be perpendicular to that transversal without being parallel
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