Take any two lines and look at their slopes.
-- If the slopes are equal, then the lines are parallel.
-- If the product of the slopes is -1, then the lines are perpendicular.
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PERPENDICULAR
perpendicular.
Any line that is not parallel to the given lines. The transversal that contains the shortest distance between the two parallel lines, is perpendicular to them.
It is impossible for parallel lines to be perpendicular. Perpendicular lines are intersecting lines, meaning that they cross each other. Parallel lines, on the other hand, are lines that never meet, no matter how far they are extended in either direction. So intersecting lines (which includes perpendicular lines) and parallel lines are exact opposites. Parallel lines will never meet or cross; they cannot be perpendicular.
Transversal lines are not parallel and so have a gradient that is different to that of the given lines.