Skew lines.
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No. Parallel lines do not intersect; perpendicular lines intersect at 90 degrees
No, never. Parallel lines are line that will NEVER intersect.
Coplanar lines that don't intersect are parallel. Lines that are not parallel and do not intersect are skew lines.
Parallel lines in the Euclidean plane do not intersect but all parallel lines in the projective plane intersect at the point at infinity.
They may also be parallel lines.