If an axiom is based on another axiom. It ceases to be an axiom and becomes a mathematical prove. From each point, it is possible to draw a line to any other point. A finite straight line can be changed into an infinite straight line. It is possible to construct a circle using any point as its center and any finite line as its radius.
Any right angle is equal to any other right angle.
For many centuries' mathematicians' thought that the fifth axiom was unnecessary and it would be possible to deduct it, using the other axioms. If we chose a straight line L1 and a point that is not a part of that line, then it is possible to draw an infinite number of lines that contain the point and are parallel to L1. By doing this they all proved that the fifth axiom is indeed an axiom and not a theorem. If we chose a straight line L1 and a point that is not a part of that line, then it is impossible to draw another line that contains the point and is parallel to L1. All the different kinds of geometry s that do not use the Euclid s axioms are then called Non Euclidean Geometry .