Geometry: Congruent Triangles
It's not enough that mathematicians explore their own individual triangles. Once we become comfortable with triangle ownership, it's in our nature to compare our triangle to all the other triangles out there. We need to know when two triangles match.
Every triangle has six parts (three angles and three sides). So the only way that two triangles can match is if they line up angle for angle, and side for side. The flip side is that if two triangles line up angle for angle, side for side, then they match.
With attention spans being what they are, most of us don't have the patience required to match up all six parts of a triangle to all six parts of another triangle. Fortunately for us, there is an easier way.
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.