There is very little in our world that is static. Living things like to move. I remember thinking how great it would be to move out of my parents' house. Looking back, I didn't realize that I had it so good; moving into my own house meant that I had to pay for rent, utilities, and food!
Geometrical figures like to move as well. They can slide along the plane, turn around, or flip upside down. They can do just one of these moves or they can do several of them in succession, depending on their ambitions. Throughout this process, however, they will keep the same size and shape. Triangles won't change into quadrilaterals or change angle measurements. They won't grow or shrink either.
That's not to say that geometric figures have to stay the same size throughout their lives. They can grow or shrink. But when they do, only their sides are allowed to change; their angle measures cannot. That means that as geometrical figures grow or shrink, they will remain similar to what they were before.
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.