Is There a Proof for Congruent Segments on Any Transversal with Parallel Lines?

[susanasarandon]

Our professor has challened us to find the proof for the following theorem:

If three parallel lines intercept congruant segments on one transversal, then they intercept congruant segments on any transversal.

He says it's not anywhere he's read. Help!

 

[aek]

I'll prove the theorem for you,

For any three parallel lines cut by a transversal, where AB = BC,
then another transversal will cut the parallel lines in the same ratio.

IF AB = BC, then DE = EF

I hope that's sufficient proof, i would of liked to shown a diagram, however, I'm limited by the medium I'm using.


AEK