The parallel postulate in Euclidean geometry says that in two dimensional space , for any given line l and point P not on l , there is exactly one line through P that does not intersect l. This line is called parallel to l. In hyperbolic geometry there are at least two such lines through P. As they do not intersect l , the parallel postulate is false . The parallel postulate in Euclidean geometry is equivalent to the statement that , in two dimensional space , for any given line l and point P not on l , there is exactly one line through P that does not intersect l ; i.e. , that is parallel to l. In hyperbolic geometry there are at least two distinct lines through P which do not intersect l , so the parallel postulate is false .