Geometry: Taking the Burden out of Proofs
Taking the Burden out of Proofs
When a kid makes exaggerated claims out on the playground, usually someone will ask the bragger to “prove it.” What follows is usually an awkward silence while the bragger thinks about how to justify his boast.
When mathematicians make exaggerated claims in a classroom, usually no one will ask them to “prove it.” In fact, most people are happier not knowing why a particular mathematical statement is true. But not mathematicians. It's not enough to brag about the properties of angles, segments, or other geometric shapes. They back up their claims whenever someone dares to doubt them.
When mathematicians are backing up their claims, they don't lead the audience on any wild goose chases. They don't get side tracked either. When mathematicians prove a statement the explanation is short, concise, and to the point. Organization is the key to writing proofs. In this section, you will learn some ways to organize your arguments so that everyone will understand them and there will be no room for doubt.
Excerpted from The Complete Idiot's Guide to Geometry © 2004 by Denise Szecsei, Ph.D.. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Alpha Books, a member of Penguin Group (USA) Inc.