No. Parallel has a specific meaning. For lines to be parallel, they have to lie in a common plane, but not touch each other. If they are skew, they still don't touch each other, but they now do not lie in a common plane.
More specifically, skew lines, by definition, are not co-planar.
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Skew lines are not parallel. Parallel lines are across from each other in some way and are exactly parallel.
Two lines that are not parallel and do not intersect are skew. If the non-intersecting lines are in the same plane then they are parallel.
Skew lines are noncoplanar; therefore they're not parallel & don't intersect.
SKEW LINES are neither parallel nor intersecting.
Two lines in two intersecting planes can be parallel, intersecting, or skew.