Euclid's fifth postulate with the o

Euclid's fifth postulate with the other four implies Playfair's postulate[edit source | editbeta]
The easiest way to show this is using the Euclid theorem (based in the fifth postulate) that states that the angles of a triangle are two right angles. Given a line and a point, construct a line perpendicular to the given one by the point, and a perpendicular to the perpendicular. This line is parallel because it cannot form a triangle. Now it can be seen that no more parallels exist because any line that forms an angle with the second one will cut the first one.[8]