Parallel lines remain the same distance apart and never intersect each other whereas other types of lines intersect each other at some point.
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Non-parallel lines intersect at some point, parallel lines don't.
Parallel lines are two 1-dimensional objects that do not meet. Parallel planes are two 2-dimensional objects that do not meet.
parallel lines never touch, never get any closer or any further apart. tangent lines touch at one point
Parallel lines never intersect and remain equal distance from each other but perpendicular lines intersect at right angles
If the distance between the lines is constant then they are parallel.