How do I prove to my professor that I didn't copy pasta another kid's work?

My buddy and I decided to work on it together as two minds would make the project work quicker and faster. Whenever we had to code, we coded separately, and compiled and ran it. Then, we saw how the other did what, and depending on who got it correct, we switched our codes to be more correct and functioning. Now, handing in the project, he states that our codes are too similar.

Unless you were allowed to collaborate, your professor has every right to be suspicious because you did copy each other in a very real sense.