Postulates are assumed to be true without proof.  See what happens when you assume one is false.

Non Euclidean Geometry

Animation by Yosi Studios demonstrating elliptic and hyperbolic geometries with their historical development.  Duration_6_05

Playing Sports in Hyperbolic Geometry

In this Numberphile video, Dick Canary explains some insane consequences of playing sports in hyperbolic geometry.  Duration_8_26

History of Non-Euclidean Geometry

This is a lecture about the development of Non-Euclidean Geometry by Norman Wildberger, a Canadian Math Professor in Australia. With that kind of geographic pedigree, you might expect more of an accent, but the strangest thing he says is "zed" instead of the letter Z. The guy is also pretty good at drawing on a chalkboard but really bad at erasing said chalkboard.  Duration_50_51 

Geometry 4(A) distinguish between undefined terms, definitions, postulates, conjectures, and theorems

Geometry 4(D) compare geometric relationships between Euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle.