Question 516751: how do you solve a geometry proof when not given the statements or the reasons? what are some tips to help me remember how to solve them? thank you.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! You have to come up with those statements and reasons yourself. I've done proof examinations such as the USAMO in which they give you no hints or information other than the question itself. The idea of a proof is mainly to formulate your own thoughts on a solution (for extremely tricky ones, they can be quite clever or innovative, or invoke unusual methods) instead of use the book's solution, which may be dull or repetitive. Proving theorems takes time, though.
Think of a proof as an argument. You are trying to prove something so you want to support your "argument" by using whichever techniques are possible. Remember to do it in a logical order, too. This works for any proof, whether it be for a simple proof of the area of a triangle, or a USAMO/IMO/other Olympiad question, or an extremely difficult problem such as P vs. NP or whether an odd perfect number exists.
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