I'm trying to be confident when meeting a woman. If I see an attractive woman randomly I'd like to just come up to her and say something. I'm not really shy I just don't know what to say. Do any of you guys have a line that introduces yourself very politely while complimenting her? I want to make my intentions known without being creepy or ambiguous. Also do you know a polite thing to say if rejected?

something along the lines of....

Hi there, how are you? I don't normally approach women like this but I wanted to say that you are very attractive.

Right then and there you can know if she's interested based on her next response. Also do you all know good lines to say afterwards to keep the conversation going such as a good question? If you guys have any good ways to initiate conversation and be friendly let me know. Also if you know nice compliments I'd like to know them as well.

There's something unrelated I'd like to ask you guys. When I go out in public a good 65%-80% of attractive women I see are with their children. Should I assume that these women are taken? Would it be rude to approach these women? I don't want to trample anyone's relationship and if they do have a boyfriend or husband I don't want any part in something like that. It's just that a huge amount of the dating pool seems to have kids. Do you know what percentage of women you meet in public who have kids are actually in a relationship something like 50%? So do you think they would find it rude if they did have a boyfriend or would they take it as a friendly compliment that would brighten their day even if they say they do have a boyfriend? Or should I just not worry about it?