Two lines will remain parallel when they are intersected by a transversal line
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No. Parallel lines do not intersect; perpendicular lines intersect at 90 degrees
Skew lines.
They may also be parallel lines.
No, they can't be, if they intersect. This is because any two lines parallel to the same line are also parallel. And since they intersect, they aren't parallel.
no. if they touch, then they cannot be parallel.