We are asked to give an indirect proof for this problem: Lines are only distinct if the contain a unique set of points. (In other words, they may share points, but they cannot share all points.) Consider a line perpendicular to a given line through a given point. Now, start at that point, and draw another line that is perpendicular. There is only one angle you can go at (namely, the angle of the original line), so the line will have the same set of points. Thus, the two lines will not be distinct.
Work Step by Step
Answer is above.