Skew lines.
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Are very common but do not have any particular name. Sit in the corner of a cuboid room. Consider one line which is defined by the floor and the wall on your left. Consider the other as that formed by the ceiling and the wall on your right.
Alternate int angles are two interior angles which lie on different parallel lines and on opposite sides of a transversal
Not sure if these are the ones that you are looking for, but here are three:Parallel lines do not intersect.Parallel lines lie in the same plane.parallel lines have the same slope.
A hexagon has parallel lines.
That is a plane.Any one of infinitely many planes.