Mark Ryan - Geometry For Dummies

Geometry For Dummies, 3rd Edition

Published by: John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, www.wiley.com

Copyright 2016 by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

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Library of Congress Control Number: 2016936127

ISBN 978-1-119-18155-2 (pbk); ISBN 978-1-119-18164-4 (ebk); ISBN 978-1-119-18156-9 (ebk)

1. Table of Contents

Geometry is a subject full of mathematical richness and beauty. The ancient Greeks were into it big-time, and its been a mainstay in secondary education for centuries. Today, no education is complete without at least some familiarity with the fundamental principles of geometry.

But geometry is also a subject that bewilders many students because its so unlike the math that theyve done before. Geometry requires you to use deductive logic in formal proofs. This process involves a special type of verbal and mathematical reasoning thats new to many students. Seeing where to go next in a proof or even where to start can be challenging. The subject also involves working with two- and three-dimensional shapes: knowing their properties, finding their areas and volumes, and picturing what they would look like when theyre moved around. This spatial reasoning element of geometry is another thing that makes it different and challenging.

Geometry For Dummies, 3rd Edition, can be a big help to you if youve hit the geometry wall. Or if youre a first-time student of geometry, it can prevent you from hitting the wall in the first place. When the world of geometry opens up to you and things start to click, you may come to really appreciate this topic, which has fascinated people for millennia and which continues to draw people to careers in art, engineering, architecture, city planning, photography, and computer animation, among others. Oh boy, I bet you can hardly wait to get started!

Geometry For Dummies, 3rd Edition, covers all the principles and formulas you need to analyze two- and three-dimensional shapes, and it gives you the skills and strategies you need to write geometry proofs. These strategies can make all the difference in the world when it comes to constructing the somewhat peculiar type of logical argument required for proofs. The non-proof parts of the book contain helpful formulas and tips that you can use anytime you need to shape up your knowledge of shapes.

My approach throughout is to explain geometry in plain English with a minimum of technical jargon. Plain English suffices for geometry because its principles, for the most part, are accessible with your common sense. I see no reason to obscure geometry concepts behind a lot of fancy-pants mathematical mumbo-jumbo. I prefer a street-smart approach.

This book, like all For Dummies books, is a reference, not a tutorial. The basic idea is that the chapters stand on their own as much as possible. So you dont have to read this book cover to cover although, of course, you might want to.

Geometry For Dummies, 3rd Edition, follows certain conventions that keep the text consistent and oh-so-easy to follow:

• Variables are in italics.
• Important math terms are often in italics and are defined when necessary. Italics are also sometimes used for emphasis.
• Important terms may be bolded when they appear as keywords within a bulleted list. I also use bold for the instructions in many-step processes.
• As in most geometry books, figures are not necessarily drawn to scale though most of them are.
• I give you game plans for many of the geometry proofs in the book. A game plan is not part of the formal solution to a proof; its just my way of showing you how to think through a proof. When I dont give you a game plan, you may want to try to come up with one of your own.

Focusing on the why in addition to the how-to can be a great aid to a solid understanding of geometry or any math topic. With that in mind, Ive put a lot of effort into discussing the underlying logic of many of the ideas in this book. I strongly recommend that you read these discussions, but if you want to cut to the chase, you can get by with reading only the example problems, the step-by-step solutions, and the definitions, theorems, tips, and warnings next to the icons.

I find the gray sidebars interesting and entertaining big surprise, I wrote them! But you can skip them without missing any essential geometry. And no, you wont be tested on that stuff.

I may be going out on a limb, but as I wrote this book, heres what I assumed about you:

• Youre a high school student (or perhaps a junior high student) currently taking a standard high schoollevel geometry course.