That's the only kind of parallel lines there are, non-intersecting!
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draw two intersecting lines that are not perpendicular
In 2D geometry, that is the definition of parallel lines. Two non-intersecting lines are indeed parallel.
The question is baffling. They're not different. Perpendicular lines must be intersecting lines.The only lines that are not intersecting lines are parallel lines. If two lines arenot parallel, then they must intersect, and they can be perpendicular or not.
Lines in the same plane that are not parallel are intersecting lines.
Draw two lines that meet somewhere