Thread: Parallel Transports

I cannot figure out the proof to this problem:

If l1 and l2 are lines on a plane such that they are parallel transports along a transversal l, then they are parallel transports along any transversal.

How would you prove this? I know the proof has to be based on a contrapositive or contradiction but I am just not sure how to do this. I started with a contradiction by assyming l1 and l2 are lines on the plane such that they are parallel transports along a transversal l, and they are not parallel transports along any other transversal.

I don't believe my contradiction is correct though. Any help would be greatly appreciated

We need to prove this by using assumptions, but it needs to be a simple as possible.

What part of this proof does not work on a hyperbolic plane?

Some suggestions to figuring this problem out are:

In order to prove this theory we need to assume something.

Any ideas??