Transcription
GEOMETRYRon LarsonLaurie BoswellTimothy D. KanoldLee Stiff
GEOMETRY
About GeometryIn Geometry, you will develop reasoning and problem solving skills as youstudy topics such as congruence and similarity, and apply properties oflines, triangles, quadrilaterals, and circles. You will also develop problemsolving skills by using length, perimeter, area, circumference, surface area,and volume to solve real-world problems.In addition to its geometry content, Geometry includes numerous examplesand exercises involving algebra, data analysis, and probability. These mathtopics often appear on standardized tests, so maintaining your familiaritywith them is important. To help you prepare for standardized tests,Geometry provides instruction and practice on standardized test questionsin a variety of formats—multiple choice, short response, extended response,and so on. Technology support for both learning geometry and preparingfor standardized tests is available at classzone.com.
Copyright 2007 McDougal Littell, a division of Houghton Mifflin Company.All rights reserved.Warning: No part of this work may be reproduced or transmitted in any form orby any means, electronic or mechanical, including photocopying and recording,or by any information storage or retrieval system without the prior writtenpermission of McDougal Littell unless such copying is expressly permitted byfederal copyright law. Address inquiries to Supervisor, Rights and Permissions,McDougal Littell, P.O. Box 1667, Evanston, IL 60204.ISBN-13: 978-0-6185-9540-2ISBN-10: 0-618-59540-6 123456789—DWO—09 08 07 06 05Internet Web Site: http://www.mcdougallittell.comiv
About the AuthorsRon Larson is a professor of mathematics at Penn StateUniversity at Erie, where he has taught since receiving his Ph.D. inmathematics from the University of Colorado. Dr. Larson is wellknown as the author of a comprehensive program for mathematicsthat spans middle school, high school, and college courses.Dr. Larson’s numerous professional activities keep him in constanttouch with the needs of teachers and supervisors. He closelyfollows developments in mathematics standards and assessment.Laurie Boswell is a mathematics teacher at The Riverside Schoolin Lyndonville, Vermont, and has taught mathematics at all levels,elementary through college. A recipient of the Presidential Awardfor Excellence in Mathematics Teaching, she was also a TandyTechnology Scholar. She served on the NCTM Board of Directors(2002–2005), and she speaks frequently at regional and nationalconferences on topics related to instructional strategies and coursecontent.Timothy D. Kanold is the superintendent of Adlai E. StevensonHigh School District 125 in Lincolnshire, Illinois. Dr. Kanold servedas a teacher and director of mathematics for 17 years prior tobecoming superintendent. He is the recipient of the PresidentialAward for Excellence in Mathematics and Science Teaching,and a past president of the Council for Presidential Awardees inMathematics. Dr. Kanold is a frequent speaker at national andinternational mathematics meetings.Lee Stiff is a professor of mathematics education in the Collegeof Education and Psychology of North Carolina State Universityat Raleigh and has taught mathematics at the high school andmiddle school levels. He served on the NCTM Board of Directorsand was elected President of NCTM for the years 2000–2002. He is arecipient of the W. W. Rankin Award for Excellence in MathematicsEducation presented by the North Carolina Council of Teachers ofMathematics.v
Advisers and ReviewersCurriculum Advisers and ReviewersviVincent J. BondiAnne PapakonstantinouMathematics Department ChairRadnor High SchoolRadnor, PADirector, School Mathematics ProjectRice UniversityHouston, TXJohn FishpawRichard ParrMathematics Department ChairAustin Academy for ExcellenceGarland, TXDirector of Educational Technology,School Mathematics ProjectRice UniversityHouston, TXMatthew C. HillKatherine G. PetersenMathematics TeacherPlains High SchoolPlains, TXMathematics TeacherHammond SchoolColumbia, SCPatrick HopfenspergerAlice RauMathematics SpecialistHomestead High SchoolMequon, WIMathematics TeacherFrancis Scott Key High SchoolUnion Bridge, MDRobin JenkinsDiane SorrelsMathematics TeacherHillcrest High SchoolSpringfield, MOMathematics Department Chairand TeacherRobert E. Lee High SchoolTyler, TX
Ohio PanelTodd BrennJeff NeumanCarlo T. TrafficanteMathematics TeacherRoosevelt High SchoolKent, OHMathematics TeacherBrunswick High SchoolBrunswick, OHMathematics TeacherAustintown Fitch High SchoolAustintown, OHSinetta MaulBruce OlsonAndrew TripoulasMathematics TeacherAshland High SchoolAshland, OHMathematics TeacherCanal Winchester High SchoolCanal Winchester, OHMathematics TeacherWarren G. HardingHigh SchoolWarren, OHCathy J. MillerJulia PfeilVicki L. WhiteMathematics TeacherCopley High SchoolCopley, OHMathematics TeacherColonel White High Schoolfor the ArtsDayton, OHMathematics TeacherStrongsville High SchoolStrongsville, OHTexas PanelNancy ArroyoWhitney HendriexShauna SuggsMathematics Department ChairRiverside High SchoolEl Paso, TXMathematics SpecialistLee High SchoolMidland, TXMathematics TeacherR.L. Turner High SchoolCarrollton, TXJuan A. CardenasBetsy A. NorrisRichard TreviñoMathematics Department ChairSam Houston High SchoolSan Antonio, TXMathematics TeacherSouthwest High SchoolFt. Worth, TXMathematics TeacherMartin High SchoolLaredo, TXRita Hines FreemanJanell O’LoughlinPatricia WinklerMathematics TeacherTownview Science and EngineeringMagnet High SchoolDallas, TXMathematics Department ChairPasadena High SchoolPasadena, TXMathematics Teacher andInstructional TechnologistMichael E. DeBakey High SchoolHouston, TXvii
CHAPTER1Unit 1Points, Lines,and PlanesSegment Addition Postulate, p. 14AC 5 AB 1 BCEssentials of GeometryPrerequisite Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii1.1 Identify Points, Lines, and Planes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Use Segments and Congruence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3 Use Midpoint and Distance Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Mixed Review of Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231.4 Measure and Classify Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Investigating Geometry Construction:Copy and Bisect Segments and Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331.5 Describe Angle Pair Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351.6 Classify Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421.7 Find Perimeter, Circumference, and Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Investigating Geometry Activity: Investigate Perimeter and Area . . . . . . . . . . . 48Problem Solving Workshop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Mixed Review of Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58ASSESSMENTQuizzes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22, 41, 56Chapter Summary and Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Algebra Review: Solve Linear Equations and Word Problems . . . . . . . . . . . . . . . . . . . . 65 Standardized Test Preparation and Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66(FPNFUSZ Activities . . . . . . . . . . . . . . . . . . . . . . . . 1, 3, 14, 21, 25, 43, 52DMBTT[POF DPNChapter 1 HighlightsPROBLEM SOLVING ASSESSMENT Mixed Review of Problem Solving,23, 58 Multiple Representations, 41, 55, 57 Multi-Step Problems, 8, 14, 23, 46, 54,55, 58 Using Alternative Methods, 57 Real-World Problem Solving Examples,10, 15, 27, 36, 44, 51, 65 Standardized Test Practice Examples,18, 50 Multiple Choice, 6, 13, 20, 29, 39, 44, 46,53 Short Response/Extended Response,7, 12, 14, 20, 22, 23, 30, 32, 40, 47, 54, 55,58, 66 Writing/Open-Ended, 5, 12, 19, 23, 28,38, 44, 52, 58viiiContentsTECHNOLOGYAt classzone.com: Animated Geometry, 1, 3, 14, 21, 25, 43,52 @Home Tutor, xxii, 7, 13, 21, 31, 40, 46,48, 54, 60 Online Quiz, 8, 14, 22, 32, 41, 47, 56 Animated Algebra (Algebra Review), 65 State Test Practice, 23, 58, 69
CHAPTER2Unit 1Points, Lines,and PlanesProperties of Congruence, p. 115}AB }CDReasoning and ProofPrerequisite Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702.1 Use Inductive Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 722.2 Analyze Conditional Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 792.3 Apply Deductive Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Investigating Geometry Activity: Logic Puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 862.4 Use Postulates and Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96Mixed Review of Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1032.5 Reason Using Properties from Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105Investigating Geometry Activity: Justify a Number Trick . . . . . . . . . . . . . . . . . . . 1042.6 Prove Statements about Segments and Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Problem Solving Workshop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1202.7 Prove Angle Pair Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124Investigating Geometry Activity: Angles and Intersecting Lines . . . . . . . . . . . 122Mixed Review of Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132ASSESSMENTQuizzes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93, 111, 131Chapter Summary and Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138Algebra Review: Simplify Rational and Radical Expressions . . . . . . . . . . . . . . . . . . . . 139 Standardized Test Preparation and Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140(FPNFUSZ Activities . . . . . . . . . . . 71, 72, 81, 88, 97, 106, 119, 125DMBTT[POF DPNChapter 2 HighlightsPROBLEM SOLVING ASSESSMENT Mixed Review of Problem Solving,103, 132 Multiple Representations, 77, 111, 120 Multi-Step Problems, 85, 102, 103, 110,119, 130, 132 Using Alternative Methods, 120 Real-World Problem Solving Examples,74, 89, 106, 115 Standardized Test Practice Examples,74, 127 Multiple Choice, 75, 76, 83, 90, 99, 100,109, 116, 128 Short Response/Extended Response,76, 78, 84, 92, 101, 102, 103, 110, 117, 119,128, 130, 132, 140 Writing/Open-Ended, 75, 82, 84, 90, 99,100, 108, 109, 116, 127, 129, 132TECHNOLOGYAt classzone.com: Animated Geometry, 71, 72, 81, 88, 97,106, 119, 125 @Home Tutor, 70, 77, 84, 91, 101, 110,118, 123, 129, 134 Online Quiz, 78, 85, 93, 102, 111, 119, 131 Animated Algebra, 139 State Test Practice, 103, 132, 143Contentsix
CHAPTER3Unit 1Points, Lines,and PlanesApplying Slope, p. 17441Slope 5 }}80Parallel andPerpendicular LinesPrerequisite Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1443.1 Identify Pairs of Lines and Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147Investigating Geometry Activity: Draw and Interpret Lines . . . . . . . . . . . . . . . . 1463.2 Use Parallel Lines and Transversals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154Investigating Geometry Activity: Parallel Lines and Angles . . . . . . . . . . . . . . . . . 1533.3 Prove Lines are Parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161Mixed Review of Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1703.4 Find and Use Slopes of Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171Technology Activity Investigate Slopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1793.5 Write and Graph Equations of Lines . . . . . . .
In Geometry, you will develop reasoning and problem solving skills as you study topics such as congruence and similarity, and apply properties of lines, triangles, quadrilaterals, and circles. You will also develop problem solving skills by using length, perimeter, area, circumference, surface area, and volume to solve real-world problems. In addition to its geometry content, Geometry includes .
