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