No.
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Two parallel lines, a plane and a line in a plane parallel to it.
Parallel lines
They can be, but not necessarily. If two lines in the same plane never intersect, they are parallel. Though, two lines can exist in the same plane without being parallel. Ie, two lines that intersect at a 90 degree angle are perpendicular. Most lines in a plane aren't parallel.
Two lines are coplanar iff they are parallel OR intersect.
parallel lines :)