Sudden interaction from attractive girl in my class

[Savagery]

Hello everyone ! I'm new here. And I'd like advice on an event that occurred to me the other day.

A girl that I've never spoken to who goes to the same school as I do suddenly interacted with me - We're both in grade 12. You see, I've never once spoken to this girl. We've never even exchanged greetings nor have I ever hung out in a group where she was included. Basically 0 interaction before - She's one of the 'popular' girls in school. Anyways, in class the other day, she was sitting 1 row behind me and as I was conversing to my friend, who was sitting in the same row as her but 3 chairs left, I noticed she was paying attention to our conversation. Specifically she was looking at me - I caught her at the edge of my eye - and then as I said something that wasn't even intended to be a joke I noticed her chuckle and smile. Despite that being very surprising, an even more surprising thing happened when class was over.

I was walking towards my mum's car once class had ended and I happened to pass by her - I was not beside her though, probably about a couple of feet away ? Maybe even a few meters - and I coincidentally looked at her and she looked at me back and proceeded to smile and wave as if she knew me when in reality we've never even spoken. And once I was in the car, my mum drove past her and she saw me through the passenger window and smiled at me and I proceeded to do the same.

I'm not sure what this all means, I'm thinking of approaching her when we have class together again and see how it goes. But I ran through all this with my friend who claims to be an 'expert' - Although his advice are good - he says that she might have an attraction toward me, but she wants me to approach her. However, my other friend says that I'm delusional and that she's just way out of my league and that I shouldn't even try. Now, I'm not an outgoing or very social person - Although I do have quite a large number of acquaintances and friends - and I've only had 3 relationships previously. So, what do ? Should I approach her ? How so ? I'm terrible at these kind of things and she's one of the 'popular' girls in school. I can't even approach a regular girl. I'd appreciate any help and advice. Thanks in advance !

[4 ratties]

Why not start with "hi how are you doing today?"