parallel lines never intersect.
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Zero; they never intersect and therefore they do not have a solution.
A quadrilateral has 4 sides, 2 in which never intersect. Therefore, the lines that don't intersect are called parallel. There are 4 parallel sides but has 2 pairs of parallel sides.
A triangle can have no parallel lines.
If rays, parallel ones. If segments there are many more options because you can have a segment that is not long enough to reach the point of intersection.
A pentagon has no parallel lines.