Why does my friend always do this?

I have this friend who always acts like she's in a competition with me even though I take no part in it. I'm kind of a "geek" in school and she feels like she always has to try to outdo me when it comes to academics. Whenever I get an award or something, while others close to me might congratulate me, she acts extremely jealous and talks about how it's not a big deal. She always tries to put me down, and often gives back-handed compliments. Whenever she says that she doesn't understand her homework, and I ask her if I can possibly help her, she gets extremely defensive and says how it's very easy. Should I just wait until we just "drift apart" or what? What can I do to make her stop? Thoughtful answers would be appreciated.