Prove that if l and m are distinct lines and there exist two different points of m that are on the same side of l and equidistant from l, then l is parallel to m. Solution Since the two points are equidistant from L , hence the length of perpendiculars from L to M are same at two points. If , we join the two lines on these two points, we form a figure which has the opposite sides equal and parallel. This can be a rectangle or a parallelogram. In either case, the two lines are parallel..