Perseo Miranda Parallel Dimensions was created in 2008.
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In two dimensions, lines can be parallel, angles cannot. So no plane shape has parallel angles.
No one knows for sure. The existence of Parallel Dimensions is as yet an unproven Theory.
In space with 3 or more dimensions, there are infinitely many pairs of lines that are not parallel and do not intersect.
Non-intersecting lines in 3-D space may be parallel but need not be.
in reality they don't exist, but are parallel universes
8 foot and 27 feet long
In two dimensions: They are parallel if their gradients are the same. They are perpendicular if the product of their gradients is -1. Otherwise they are neither. The nature of the question suggests that you have not yet studied lines in 3 or more dimensions.