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the parallel lines never intercept so they do not have any common points.
No, parallel lines never intersect, so they do not have any points in common. Intersecting lines have one common point.
If two lines cross they share a point of intersection. For two straight lines this is limited to one common point, for two circles two points and for complex lines like two sine waves the number of common points has no limit.
Parallel lines lying in a plane do not intersect each other. They share exactly zero points in common.
Zero. A null angle is formed by two straight lines that coincide.