This may sound shallow, but human beings, and basically all of nature, are not meant to be in monogamous relationships; at least biologically. This is what makes relationships such a challenge.
It's difficult, but I would break up with a girl before I felt like cheating on her. A lot of people throw the word cheating around loosely, but I wouldn't want to be cheated on in any way, especially if it was being hidden from me. I'd never want to be hurt like that, so I consider any girl I think is relationship potential as my only for as long as it lasts.