Message #237800

[MsRowdyRedhead]

THERE IS NEVER JUST ONE WAY OF STATING A PROOF.
The two most important things a proof must possess are clarity and backup.
Actually there are even several ways of presenting a proof argument:

   1. There is the high school textbook, classic, method of writing two columns, the first being a list of numbered arguments and the second column a matching list of legal justifications i.e. theorems, definitions, postulates.
     
   2. Then there is the more "collegiate" method of writing a lengthy paragraph. This is known as the paragraph method and each sentence is backed up in prose form with its justification.
     
   3. In the American Society of Professional Estimators, we use a mixture of the two. We write numbered, complete, sentences which each have a legal math reason imbedded in them. Our most important goals are KEEP IT EASY TO UNDERSTAND and KEEP IT LEGAL.
 

So don't worry about trying to match a "perfect wording". Just be sure that your statements are clear, and that they are each backed up with a legal reason.

A good measure of the quality of your proof is found by reading it to a person who has not taken a geometry course or who hasn't been in one for a long time. If they can understand your proof by just reading it, and they don't need any verbal explanation from you, then you have a good proof.

It's fun once you get good at it, and being good at it makes your powers of reason MUCH stronger. No, you will probably never need to prove that a rhombus is a convex quadrilateral in "real life", but learning how to do it will develop a strong logical circuit in your brain.