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Ask her on a "casual date" with other friends or a group of people. Be yourself, even if you are shy. Ask a mutual friend for advice. Note her body language around you.
This is usually a good way to gauge your relationship without the pressure of an intimate date. If you're having a get together with friends or going out to a club, ask her along or have a friend invite her. This way you can see each other in a social setting. Does she spend time with you? Do you have fun together? Trying to fake someone into liking you is a sure-fire way to start a failing relationship. You have to have confidence in who you are. If she doesn't like that, then you would not have made a very happy couple anyway. Feel more confident by focusing less on yourself and more on her. Someone on the outside can give you valuable perspective on her feelings for you, and give some advice on how to proceed. Find a friend you trust and confide in them to see how they see things. Do they think you would make a good couple? Do they think the feelings are mutual? How would they talk to her about your feelings? This can be a "practice round," helping you sort out your feelings. Does she make eye contact, hug or touch you, lean in when you talk, or sit next to you whenever possible? These are all good signs that she may have similar feelings. Closing her body off by folding her arms, avoiding eye-contact, or making excuses not to talk are often signs that she is not interested.