Girl sits next to me in class, I like her but can't find it in me to say something

Kenival
Well, ever since college started I have a class that's only 2 days a week. Every time I'm in class there this really cute girl sitting, usually, a seat away from me. I don't know how to start talking to her. I can't start a conversation in the middle of class because our professor is extremely strict and if you do something he doesn't like, he will put you on the spot in front of the whole class, I don't want that happening.. I don't want to embarrass her or myself.

I came to class early today to see if maybe I'd find the balls to start talking her but I did not. I was going to sit in the seat right next to her but I didn't want to creep her out so I sat a seat over, like we usually do. We had about 10 minutes of free time and I just couldn't say anything to her.. don't know why, I'm not that shy of a guy. So I completely failed..

But last Tuesday she was a bit late to class and she sat in the seat right next to me even though there was room on either side.. maybe it was just the seat she always sits in, or maybe she wants me to talk to her.

I very much would like to start talking to her.. maybe offer her a ride home or something but I cannot for some reason.

Guys, please help =[
Girl sits next to me in class, I like her but can't find it in me to say something
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