1. Play fair’s Axiom
This says that if you have a line ‘l’ and a point P which doesn’t lie on line ‘l’ then there could be only one line passing through point P which will be parallel to line ‘l’. No other line could be parallel to line ‘l’ and passes through point P.
2. Two distinct intersecting lines cannot be parallel to the same line.
This also states that if two lines are intersecting with each other than a line parallel to one of them could not be parallel to the other intersecting line.