Question

Given a line segment AB and a point C not on it, using appropriate axiom show that there is only one perpendicular from C on AB.​

Answer 1

Let M

C and MD

Let MC and MD be two distinct perpendiculars, i.e. m∠MCA=m∠MDA=90°. Then, according to the corresponding angles theorem, MC is parallel to MD. But parallel lines do not have common points (point M belongs to both lines). Contradiction.