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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   

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   
Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry

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