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Provided the two lines are constantly the same space apart, then they can be classed as being parallel, no matter how twisted the two lines are.
Two vertical lines, next to each other.
Two non-parallel lines in space that do not intersect are called skew lines. The skew line symbol is a short horizontal bar above the two identifying letters.
They can be, but not necessarily. If two lines in the same plane never intersect, they are parallel. Though, two lines can exist in the same plane without being parallel. Ie, two lines that intersect at a 90 degree angle are perpendicular. Most lines in a plane aren't parallel.
A transversal is a line that intersects two or more other lines. If the corresponding angles are congruent then the two lines being intersected are parallel and vice verso.