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### More on Geometry Proofs

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Date: 12/11/2001 at 16:18:11
From: Cherie
Subject: Geometry proofs

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.

```

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Date: 12/11/2001 at 23:27:06
From: Doctor Peterson
Subject: Re: Geometry proofs

Hi, Cherie.

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

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