if a girl checks you out a bit from about 50 feet away...then you check her out a bit...then she looks down at the pavement until you pass. Is that basically saying I checked you out, you weren't for me so dont bother approaching?

First, your thinking as a guy would think. Yes girls are attracted by looks but they are also able to grow an attraction with a guy through personality. Whereas us guys are very shallow!

Second, she looked at you. Girls are usually quite subtle at checking guys out, sounds like you caught her.

Third, a girl doesn´t really know what she wants. A guy can approach a girl without even being checked out or anything and within 5 minutes, the girl can start fancying the guy. Girls love guys with personality. This is so true.

Fourth, she looked at you and looked down. Sounds like she is submissive to you. Would have been a good approach and many fun nights to be honest! Just don´t hold back next time!

You could have even said to her, "Hey I saw you checking me out so I wanted to say hi" ... it puts it on her. She´ll find it funny, of course she´ll deny it but you just ignore that and have a convo with her

Not necessarily. She might be shy. You can crack a joke and break the ice.