Show that in an absolute geometry Euclid's fifth postulate is equivalent to|BAP|=|XPA|=|Y PZ|= 180|APZ| for all points A, B, P, X, Y, Z so that (a) A, B, P are not collinear (b) P lies between X, Z (c) P is between A, Y, (d )X and B lie in opposite half-planes of AP (e)AB is parallel to XZ.