Two straight lines that are equidistance from each other.
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Parallel lines by definition never cross each other.
No angles are formed on the inside of parallel lines because they do not intersect. That is the definition of parallel.
In Euclidian geometry, which is the geometry of a plane surface, parallel lines do not intersect because that is the definition of parallel lines. But note that there are other geometrical systems in which parallel lines do intersect, for example if they are drawn on the surface of a sphere. Definition of parallel lines: Lines that always stay the same distance apart and never meet.
In 2D geometry, that is the definition of parallel lines. Two non-intersecting lines are indeed parallel.
A transversal line cutting through parallel lines creates various angles