Geometric Proofs---Help

greatwhiteshark

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May 8, 2005
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279
There are two kinds of proofs: direct and indirect.

We are learning to proof geometry using what is called the TWO-COLUMN METHOD. On the left side is the statement and on the right side the reason. I often DO NOT know which part of a geometric shape to prove first or in what order the shape should be proven.

Questions:

1) Does it really matter what order the statement section is proven?

2) What exactly do I need to memorize in order to be successful when proving geometric shapes?

3) What is the difference between indirect and direct geometric proofs?

Below is a sample question. I have NO CLUE where to begin. I notice that there are proofs that require more statements and reasons than others.

Here is a sample question:

Given:

C is the midpoint of segment AD.
C is the midpoint of segment BE.

Prove: Triangle ABC is congruent to Triangle DEC

This has been my biggest challenge in math. This is worst than word problems. I have NO CLUE how to tackle this type of question. I am frustrated. Help.

MY WORK:

Statement Reason
C is the midpoint of AD. Given
C is the midpoint os BE. Given

Where do I go from here? I have been fighting with proofs for months but to NO AVAIL. What is the easiest way to tackle geometric proofs?
How do I finish the question above?
 
Start with a sketch. The only advice on that is try not to assume anything that isn't there. In this one don't assume right triangles.
You have (scalene?) triangle ABC. Draw it. It is implied that BC extends to E. Draw that making BC (roughly) = CE. Same with AD. Connect DE. You have your two triangles. Mark BC = CE
----|----
and AC = CD
----||----
Now you have to know what proves congruance.
SSS? You don't know anything about side AB so that probably isn't it.
ASA You don't know anything about angles A or B so that probably isn't it.
SAS Aha! We know something about two sides and the included angle. Now you know where you are going so you need to know why AC = CE (mid points) and >BCA = >DCE (supplementary).
Now you include ASA and you have it.
 
Does it really matter what order the statement section is proven?

Yes. At least some of the lines in your proof should be results of lines above it. The first line should usually be what you are given, and the last line should be what you are trying to prove.

What exactly do I need to memorize in order to be successful when proving geometric shapes?

Definitions and postulates. It might be okay to memorize some theorems too, but I'd try to avoid that as much as you can. Instead, try really to make sense of them and understand them intuitively. That way, it will be easier to see where to use them than if you just memorize them word-for-word.

What is the easiest way to tackle geometric proofs?

I find it helpful to draw a picture and ask myself "Why must this be true?". Try to draw the picture in such a way that what you are given is true, but what you are trying to prove is false. When you find that you can't, you might see why. Then it's a matter of explaining it with theorems and postulates. If you find that you can draw the picture accurately such that what is given is true and what you are to prove is false, then it is impossible to prove.
 
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