More on Geometry Proofs
Date: 12/11/2001 at 16:18:11 From: Cherie Subject: Geometry proofs I have tried reading your proof questions and answers on the already asked questions and they aren't helping me. My problem with geometric proofs is that I don't understand how to get from the given to the prove part. AND all the statements sound the same - if I write "transitive," it ends up being "substitution," or vice-versa. The weird thing is I understand algebraic proofs fine. I can do those without a problem. Please help me. Thanks.
Date: 12/11/2001 at 23:27:06 From: Doctor Peterson Subject: Re: Geometry proofs Hi, Cherie. Your kind of question is one of the harder ones to answer about proofs, because it's hard to make it specific enough to answer. It's easiest if you can give me a particular proof, show me what you did, and point out which parts you are unsure of. Then we can go through it and probably help more, as I tried to do here: Geometry Proofs http://mathforum.org/dr.math/problems/victoria.11.07.01.html It sounds as if your main trouble is in choosing the right reason to give for a statement that you know is true. I recommend not worrying too much about that; the really important steps usually have definite names (like "SAS theorem"), while it's the little details that are hard to identify, and I don't think you should focus on those parts and miss the big picture of a proof. Unfortunately, many teachers want you to get all the details just right. In that case, they owe you a list of names to use, and a clear explanation of just what each one means. Some good geometry books do that. If yours doesn't, you should make your own list of basic theorems and axioms (such as transitivity) and write a clear statement of the exact meaning of each. Then any statement that fits an axiom can be explained by that reason. You will find some ideas along this line in the answer I referred to above. The distinction between "transitive" and "substitution" is a good example of that. I think often the ideas overlap, and a good case could be made for using either one. I would use "transitivity" when two previous statments say explicitly that A = B and B = C, and I want to say A = C. That is what the term means. I could think of that as substitution (replacing B in the first equality with C), but that term is better used in more general cases, as when you know that A = B+C and that C = D, and want to say A = B+D. Here transitivity isn't directly involved. If you need any more help, feel free to write back any time. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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