You would get a set of angles whose interrelationships would be more complex.
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Railway lines with sleepers? Lines of latitude crossed by a line of longitude?
a transversal line If a transversal intersects two parallel lines, then the alternate interior angles are congruent.
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.
Transversal lines are not parallel and so have a gradient that is different to that of the given lines.
The transversal line cuts through the parallel lines that are equal distance apart and never meet together.