any direction they just run alongside each other
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yes
Parallel is when they are facing the same way eg. | | OR - -
The lines have to intersect because lines go on forever and if then are not parallel then they will collide. Even if they are not parallel by one degree they will still intersect.
No, But 1 Dimensional Does. The lines may or may not go on forever but that has no effect on whether or not a parallel line will cross.
The simplest way is to construct a square which has two pairs of equal opposite parallel lines