HG 36
T60. Two lines will be parallel, with a common perpendicular, if there is a transversal which cuts the lines so as to form equal alternate interior angles or equal corresponding angles.
T61. If two lines have a common perpendicular, there are transversals which cut the lines so as to form alternate interior angles (or equal corresponding angles). The only transversals which have this property are those which go through the point on that perpendicular which is midway between the lines.