Table Of Content

Study Aids/Mathematics $16.95 1 0 Increase Your Geometry Skills and Score Higher on 5 5 Free Access to Any Standardized Test! 0 1 Additional Online G Practice Exercises— This comprehensive study guide takes you step-by-step though 501 geometry questions, e helping you brush up on your math skills, gain effective problem-solving techniques, o with m and prepare for academic exams. Each question is accompanied by a complete answer Instant Scoring! e explanation, so you can clearly see what you did right and in what areas you need t r to improve. y Q G 501 Geometry Questions will help you: u e EOMETRY s 4 Learn math concepts and properties, including trigonometry basics t i o n 4 Work with lines and angles s 4 Identify and classify shapes Q UESTIONS A 4 Determine ratios, proportions, perimeters, and surface measures d d e d 4 Assess your geometry skill level and boost your V a lu abilities in key areas e — F r e e O n 2nd EDITION—COMPLETELY REVISED AND UPDATED! FREE Geometry Practice Online! lin e P r a Visit LearningExpress’s Online Practice Center to: c 4 Complete coverage of geometry concepts t ic e covered on the SAT, ACT, GRE, GMAT, and 4 Access additional geometry practice exercises w ith other standardized tests 4 Receive immediate scoring and detailed answer explanations I n s t a 4 Focus your study with our customized diagnostic report n t 4 Improve your skills with targeted S c o practice and detailed answer explanations r in g ! 4 Build test-taking confidence—fast! Prepare for a Brighter Future 501 GEOMETRY QUESTIONS.indd 1 3/7/12 9:41 AM 7233_501 Geometry(2n#58F5F2.qxd 3/8/12 4:17 PM Page i 55 00 11 G EOMETRY Q UESTIONS 7233_501 Geometry(2n#58F5F2.qxd 3/8/12 4:17 PM Page ii 7233_501 Geometry(2n#58F5F2.qxd 3/8/12 4:17 PM Page iii 00 11 5 5 G EOMETRY Q UESTIONS 2nd Edition ® NEW YORK 7233_501 Geometry(2n#58F5F2.qxd 3/8/12 4:17 PM Page iv Copyright © 2012 LearningExpress, LLC. All rights reserved under International and Pan-American Copyright Conventions. Published in the United States by LearningExpress, LLC, New York. ISBN 978-1-57685-894-3 Printed in the United States of America 9 8 7 6 5 4 3 2 1 Second Edition For more information or to place an order, contact LearningExpress at: 2 Rector Street 26th Floor New York, NY 10006 Or visit us at: www.learningexpressllc.com 7233_501 Geometry(2n#58F5F2.qxd 3/8/12 4:17 PM Page v Contents Introduction vii 1 The Basic Building Blocks of Geometry 1 2 Types of Angles 15 3 Working with Lines 25 4 Measuring Angles 39 5 Pairs of Angles 49 6 Types of Triangles 59 7 Congruent Triangles 73 8 Ratio,Proportion,and Similarity 87 9 Triangles and the Pythagorean Theorem 103 10 Properties of Polygons 117 11 Quadrilaterals 129 12 Perimeter of Polygons 139 13 Area of Polygons 153 14 Surface Area of Prisms 173 15 Volume of Prisms and Pyramids 183 16 Introduction to Circles and Arcs 199 7233_501 Geometry(2n#58F5F2.qxd 3/8/12 4:17 PM Page vi 501 Geometry Questions 17 Circumference and Area of Circles 213 18 Working with Cylinders,Cones,and Spheres 229 19 Coordinate Geometry 241 20 The Slope of a Line 255 21 The Equation of a Line 269 22 Transformations,Reflections,Translations, 283 and Rotations vi 7233_501 Geometry(2n#58F5F2.qxd 3/8/12 4:17 PM Page vii Introduction Geometry is the studyof figures in space. As you study geometry, you will measure these figures and determine how they relate to each other and the space they are in. To work with geometry you must understand the dif- ference between representations on the page and the figures they symbol- ize. What you see is not always what is there. In space, lines define a square; on the page, four distinct black marks define a square. What is the differ- ence? On the page, lines are visible. In space, lines are invisible because lines do not occupy space, in and of themselves. Let this be your first lesson in geometry: appearances may deceive. Sadly, for those of you who love the challenge of proving the validity of geometric postulates and theorems—the statements that define the rules of geometry—this book is not for you. It will not address geometric proofs or zigzag through tricky logic problems, but it will focus on the practical appli- cation of geometry towards solving planar (two-dimensional) spatial puz- zles. As you use this book, you will work under the assumption that every definition, every postulate, and every theorem is “infallibly” true. 7233_501 Geometry(2n#58F5F2.qxd 3/8/12 4:17 PM Page viii 501 Geometry Questions How to Use This Book Review the introduction to each chapter before answering the questions in that chapter. Problems toward the end of this book will demand that you apply multiple lessons to solve a question, so be sure you know the pre- ceding chapters well. Take your time; refer to the introductions of each chapter as frequently as you need to, and be sure you understand the answer explanations at the end of each section. This book provides the practice; you provide the initiative and perseverance. Author’s Note Some geometry books read like instructions on how to launch satellites into space. While geometry is essential to launching NASA space probes, a geometry book should read like instructions on how to make a peanut but- ter and jelly sandwich. It’s not that hard, and after you are done, you should be able to enjoy the product of your labor. Work through this book, enjoy some pb & j, and soon you too can launch space missions if you want. viii 7233_501 Geometry(2n#58F5F2.qxd 3/8/12 4:17 PM Page ix 55 00 11 G EOMETRY Q UESTIONS