1. ## Parallelism

Prove if L is a line and P is a point that is not in L, then there is a line that has P in it and is parallel to L.

2. Parallel PostulateIf there is a line and a point not on the line, then there exists one line through the point parallel to the given line.

Postulates are assumed to be true without proof.

3. Originally Posted by ntdg
Prove if L is a line and P is a point that is not in L, then there is a line that has P in it and is parallel to L.
You cannot prove that with the other 4 postulates. It depends whether you accept this statement as true or false. If you accept it as true you are playing around in Euclidean geometry. Otherwise you leave the realm of Euclidean geometry and are now in different geometries.

Maybe the question is to prove the the equivalence of Euclid's original postulate and Playfair's postulate (as you stated it above).

4. Originally Posted by masters
Parallel PostulateIf there is a line and a point not on the line, then there exists one line through the point parallel to the given line.

Postulates are assumed to be true without proof.
There are different versions of the parallel postulate though. For example:
1) "The sum of the angles in every triangle is 180 degrees."

2) "There exists a pair of straight lines that are at constant distance from each other."

3) "If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles."

Just to name three. It may be that ntdg is required to prove his/her statement from one of these.

-Dan