Formal proof for the theorem of corresponding angles

[ScientificMind]

Recently I started looking back at some basic mathematical principles, and I started thinking about the theorem of corresponding angles. It's such a basic idea that it seems obvious on an intuitive level, but despite that (or possibly because of that) I can't think of a good way to formally prove it and I haven't been able to find a formal proof online yet either. The closest I have been able to get is this page by the University of Georgia:
http://jwilson.coe.uga.edu/EMAT6680/Dunbar/Math7200/ParallelLines/parallel_corr.htm
the problem is that that proof relies on the same side interior angles theorem,
http://jwilson.coe.uga.edu/EMAT6680/Dunbar/Math7200/ParallelLines/parallel_sameside.htm
their proof for the same side interior angles theorem relies on the alternate interior angles theorem,
http://jwilson.coe.uga.edu/EMAT6680/Dunbar/Math7200/ParallelLines/parallel_altint.htm
and their proof for the alternate interior angles theorem relies on the corresponding angle theorem,
which, ultimately, means that their proof for the corresponding angle theorem relies on circular reasoning.
Does anyone have a proof for or a source with a proof for the corresponding angle theorem?

 

[YoungPhysicist]

What I think is that, you can first cut the intersection to two parts, then the two parallel lines will become two exact same figures,which the angle will be the same.