There is an infinite number of lines.
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A triangle? Three lines that intersect in three points.
Parallel straight lines never intersect.
If the 2 lines lie in the same plane, and they are not parallel, then they will intersect at some point. If the 2 lines are skew lines, then they are not in the same plane, and they will not intersect (but they are Not Parallel)
If they are in the same plane, two lines that don't intersect are said to be "parallel".
Zero; parallel lines never intersect.