FTP, identify this axiom of Euclid.
Equivalents include assuming three non-collinear points always lie on a circle.  Or that the sum of the angles of a triangle is equal to two right angles.  Unproven for over two millenia, in the 19th century it was realized that not assuming its truth led to the hyperbolic geometries of Gauss, Bolyai, and Lobachevsky.  FTP, identify this axiom of Euclid.
Equivalents include assuming three non-collinear points always lie on a circle.  
parallel (or fifth) axiom