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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.
They do not have any specific name.
Transversal lines are not parallel and so have a gradient that is different to that of the given lines.
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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.