Geometry: Proving Segment and Angle Relationships
Proving Segment and Angle Relationships
You're ready to start making claims about segments and angles. Remember that you can be asked at any time to put your money where your mouth is and prove that what you say is true. Because mathematicians never exaggerate about the one that got away, there will be plenty of evidence to support your statements and persuade any skeptic to buy your claims.
Your claims will be your theorems, and you will back every claim with a two-column proof. In this section, I will walk you through each of the five steps needed to write a formal proof. I will repeat myself over and over and over again, not because I like to type the same words repeatedly, but so that writing proofs becomes second nature. You will reach a point when you will become psychic … you'll know what's next before you turn the page. When that happens (or at least by the time you finish reading this section), you will be able to crank out a formal proof like you've been doing it all of your life.
I'll start by establishing some facts about midpoints, and then move into the realm of angles. You'll get a chance to review some postulates and definitions, and move closer to becoming good friends with algebra.
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.