My GF is ugly and her friend is HOT HELP!!??

My man, I can promise you that if you do something with "the friend" that it's going to get back to your girlfriend. Your only hope is to make it a my-word-verses-hers situation. So if you do hang out, take her to your room or some place where no one else will see you two together. Then when your girlfriend confronts you, you can be like, "yeah she came by to help me with my homework. Anything else she says is a complete lie." That's probably your best hope.