Lines and Angles School Academic... · Prerequisite Skills • Getting Started 235 • Getting Ready for the Next Lesson 245, 254, 260, 266 Study Organizer235 Reading and Writing

Snapshots 16

Standardized Test Practice • Multiple Choice 11, 19, 23, 25, 27, 35, 43, 50, 57, 58

• Short Response/Grid In 43, 50, 59

• Extended Response 59

Constructions 15, 18, 24, 31, 33, 44

Study Organizer 5

Reading and Writing Mathematics • Describing What You See 12

• Reading Math Tips 6, 29, 45, 46

• Writing in Math 11, 19, 27, 35, 43, 50

Prerequisite Skills • Getting Started 5

• Getting Ready for the Next Lesson 11, 19, 27, 36, 43

vii

Table of Contents

Lines and Angles 2

Chapter Points, Lines, Planes, and Angles 4

1-1 Points, Lines, and Planes ..................................................6

1-2 Linear Measure and Precision .......................................13

Practice Quiz 1: Lessons 1-1 and 1-2............................19

Geometry Activity: Probability and Segment Measure ........................................................20

1-3 Distance and Midpoints .................................................21

Geometry Activity: Modeling the Pythagorean Theorem.................................................28

1-4 Angle Measure.................................................................29

Practice Quiz 2: Lessons 1-3 and 1-4............................36

1-5 Angle Relationships ........................................................37

Geometry Activity: Constructing Perpendiculars .....44

1-6 Polygons............................................................................45

Geometry Software Investigation:Measuring Polygons ...................................................51

Study Guide and Review ..............................................53

Practice Test.....................................................................57

Standardized Test Practice...........................................58

• Introduction 3

• Follow-Ups 23, 65, 155

• Culmination 164

Lesson 1-5, p. 37

Jason Hawkes/CORBIS

Unit 1Unit 1

viii

Chapter Reasoning and Proof 60

2-1 Inductive Reasoning and Conjecture ...........................62

2-2 Logic ..................................................................................67

2-3 Conditional Statements ..................................................75

Practice Quiz 1: Lessons 2-1 through 2-3 ....................80

2-4 Deductive Reasoning ......................................................82

Geometry Activity: Matrix Logic..................................88

2-5 Postulates and Paragraph Proofs ..................................89

2-6 Algebraic Proof ................................................................94

Practice Quiz 2: Lessons 2-4 through 2-6 ..................100

2-7 Proving Segment Relationships ..................................101

2-8 Proving Angle Relationships.......................................107

Study Guide and Review ............................................115

Practice Test ..................................................................121

Standardized Test Practice ........................................122

Prerequisite Skills • Getting Started 61

• Getting Ready for the Next Lesson 66, 74, 80, 87, 93, 100, 106

Study Organizer 61

Reading and WritingMathematics • Biconditional Statements 81

• Reading Math Tips 75

• Writing in Math 66, 74, 79, 86, 93,99, 106, 114

Standardized Test Practice • Multiple Choice 66, 74, 80, 86, 87,

93, 96, 97, 99, 106, 114, 121, 122

• Short Response/Grid In 106, 123

• Extended Response 123

Snapshots 63

Lesson 2-3, p. 79

Galen Rowell/CORBIS

Unit 1Unit 1

ix

Chapter Parallel and Perpendicular Lines 124

3-1 Parallel Lines and Transversals...................................126

Geometry Software Investigation: Angles and Parallel Lines ........................................132

3-2 Angles and Parallel Lines ............................................133

Practice Quiz 1: Lessons 3-1 and 3-2 .........................138

3-3 Slopes of Lines ...............................................................139

3-4 Equations of Lines.........................................................145

Practice Quiz 2: Lessons 3-3 and 3-4 .........................150

3-5 Proving Lines Parallel...................................................151

Graphing Calculator Investigation: Points of Intersection ................................................158

3-6 Perpendiculars and Distance.......................................159

Geometry Activity: Non-Euclidean Geometry.........165

Study Guide and Review ............................................167

Practice Test ..................................................................171

Standardized Test Practice ........................................172

Snapshots 143

Standardized Test Practice• Multiple Choice 131, 138, 144, 149, 157, 164, 171, 172

• Short Response/Grid In 131, 135, 136, 164, 173

• Extended Response 173

Constructions 151, 160

Study Organizer 125

Reading and Writing Mathematics • Writing in Math 130, 138, 144, 149, 157, 164

Prerequisite Skills• Getting Started 125

• Getting Ready for the Next Lesson 131, 138, 144,150, 157

Lesson 3-6, p. 163

Lonnie Duka/Index Stock Imagery/PictureQuest

Snapshots 206

Standardized Test Practice • Multiple Choice 183, 191, 198, 206, 213, 217, 219,

221, 226, 231, 232

• Short Response/Grid In 233

• Extended Response 233

Constructions 200, 202, 207, 214

Study Organizer 177

Reading and Writing Mathematics • Making Concept Maps 199

• Reading Math Tips 186, 207

• Writing in Math 183, 191, 198, 205, 213, 221, 226

Prerequisite Skills • Getting Started 177

• Getting Ready for the Next Lesson 183, 191, 198, 206,213, 221

Triangles 174

x

• Introduction 175

• Follow-Ups 218, 241, 325, 347

• Culmination 390

Chapter Congruent Triangles 176

Lesson 4-4, p. 204

4-1 Classifying Triangles.....................................................178

Geometry Activity: Angles of Triangles ....................184

4-2 Angles of Triangles .......................................................185

4-3 Congruent Triangles .....................................................192

Practice Quiz 1: Lessons 4-1 through 4-3 ..................198

4-4 Proving Congruence—SSS, SAS .................................200

4-5 Proving Congruence—ASA, AAS...............................207

Geometry Activity: Congruence in Right Triangles...........................................................214

4-6 Isosceles Triangles .........................................................216

Practice Quiz 2: Lessons 4-4 through 4-6 ..................221

4-7 Triangles and Coordinate Proof .................................222

Study Guide and Review ............................................227

Practice Test ..................................................................231

Standardized Test Practice ........................................232

Elaine Thompson/AP/Wide World Photos

Prerequisite Skills• Getting Started 235

• Getting Ready for the Next Lesson245, 254, 260, 266

Study Organizer 235

Reading and WritingMathematics • Math Words and Everyday Words 246

• Writing in Math 245, 253, 260,265, 273

Unit 2Unit 2

xi

Chapter Relationships in Triangles 234

Geometry Activity: Bisectors, Medians, and Altitudes..............................................................236

5-1 Bisectors, Medians, and Altitudes ..............................238

5-2 Inequalities and Triangles ............................................247

Practice Quiz 1: Lessons 5-1 and 5-2 .........................254

5-3 Indirect Proof .................................................................255

5-4 The Triangle Inequality ................................................261

Practice Quiz 2: Lessons 5-3 and 5-4 .........................266

5-5 Inequalities Involving Two Triangles ........................267

Study Guide and Review ............................................274

Practice Test ..................................................................277

Standardized Test Practice ........................................278

Lesson 5-5, p. 267

Standardized Test Practice• Multiple Choice 245, 253, 260,

262, 264, 265, 273, 277, 278

• Short Response/Grid In 279

• Extended Response 279

Snapshots 259

Constructions 236, 237

Jeremy Walker/Getty Images

Prerequisite Skills• Getting Started 281

• Getting Ready for the Next Lesson287, 297, 306, 315, 323

Study Organizer 281

Reading and WritingMathematics • Reading Math Tips 283

• Writing in Math 286, 296, 305,314, 322, 330

Standardized Test Practice• Multiple Choice 282, 287, 297,

305, 314, 322, 331, 337, 338

• Short Response/Grid In 285, 287,314, 322, 331, 339

• Extended Response 339

Constructions 311, 314

Snapshots 296

Unit 2Unit 2

xii

Chapter Proportions and Similarity 280

6-1 Proportions.....................................................................282

Spreadsheet Investigation: Fibonacci Sequence and Ratios .................................................288

6-2 Similar Polygons............................................................289

6-3 Similar Triangles............................................................298

Practice Quiz 1: Lessons 6-1 through 6-3 ..................306

6-4 Parallel Lines and Proportional Parts ........................307

6-5 Parts of Similar Triangles .............................................316

Practice Quiz 2: Lessons 6-4 and 6-5 .........................323

Geometry Activity: Sierpinski Triangle ....................324

6-6 Fractals and Self-Similarity .........................................325

Study Guide and Review ............................................332

Practice Test ..................................................................337

Standardized Test Practice ........................................338

Lesson 6-3, p. 305

Lawrence Migdale/Stock Boston

Unit 2Unit 2

xiii

Chapter Right Triangles andTrigonometry 340

7-1 Geometric Mean ............................................................342

Geometry Activity: The Pythagorean Theorem .......349

7-2 The Pythagorean Theorem and Its Converse ...........350

7-3 Special Right Triangles .................................................357

Practice Quiz 1: Lessons 7-1 through 7-3 ..................363

7-4 Trigonometry .................................................................364

7-5 Angles of Elevation and Depression ..........................371

7-6 The Law of Sines ...........................................................377

Practice Quiz 2: Lessons 7-4 through 7-6 ..................383

Geometry Software Investigation: The Ambiguous Case of the Law of Sines.............384

7-7 The Law of Cosines ......................................................385

Geometry Activity: Trigonometric Identities............391

Study Guide and Review ............................................392

Practice Test ..................................................................397

Standardized Test Practice ........................................398

Prerequisite Skills • Getting Started 341

• Getting Ready for the Next Lesson348, 356, 363, 370, 376, 383

Study Organizer 341

Reading and WritingMathematics• Reading Math Tips 364

• Writing in Math 348, 356, 362, 369,375, 382, 389

Standardized Test Practice • Multiple Choice 348, 356, 362,

370, 376, 382, 390, 397, 398

• Short Response/Grid In 362, 372,373, 382, 399

• Extended Response 399

Snapshots 347

Lesson 7-2, p. 350

Alexandra Michaels/Getty Images

• Introduction 401

• Follow-Ups 444, 469, 527

• Culmination 580

Snapshots 411

Standardized Test Practice • Multiple Choice 409, 413, 414, 416, 423, 430, 437,

445, 451, 457, 458

• Short Response/Grid In 409, 416, 444, 459

• Extended Response 459

Constructions 425, 433, 435, 438, 441, 444

Study Organizer 403

Reading and Writing Mathematics • Hierarchy of Polygons 446

• Reading Math Tips 411, 432

• Writing in Math 409, 416, 422, 430, 436, 444, 451

Prerequisite Skills • Getting Started 403

• Getting Ready for the Next Lesson 409, 416, 423, 430,437, 445

Quadrilaterals and Circles 400

Chapter Quadrilaterals 402

8-1 Angles of Polygons .......................................................404

Spreadsheet Investigation: Angles of Polygons ....410

8-2 Parallelograms ...............................................................411

8-3 Tests for Parallelograms ...............................................417

Practice Quiz 1: Lessons 8-1 through 8-3 ..................423

8-4 Rectangles.......................................................................424

8-5 Rhombi and Squares.....................................................431

Geometry Activity: Kites .............................................438

8-6 Trapezoids ......................................................................439

Practice Quiz 2: Lessons 8-4 through 8-6 ..................445

8-7 Coordinate Proof with Quadrilaterals ......................447

Study Guide and Review ............................................452

Practice Test ..................................................................457

Standardized Test Practice ........................................458

xiv

Lesson 8-4, p. 429

Izzet Keribar/Lonely Planet Images

Prerequisite Skills• Getting Started 461

• Getting Ready for the Next Lesson469, 475, 482, 488, 497, 505

Study Organizer 461

Reading and WritingMathematics • Reading Math Tips 464, 470, 483

• Writing in Math 469, 474, 481, 487,496, 505, 511

Standardized Test Practice• Multiple Choice 469, 475, 481,

487, 493, 494, 496, 505, 511,517, 518

• Short Response/Grid In 511, 519

• Extended Response 519

Snapshots 474

Unit 3Unit 3

Chapter Transformations 460

Geometry Activity: Transformations .........................462

9-1 Reflections ......................................................................463

9-2 Translations ....................................................................470

9-3 Rotations .........................................................................476

Practice Quiz 1: Lessons 9-1 through 9-3 ..................482

9-4 Tessellations ...................................................................483

Geometry Activity: Tessellations and Transformations.........................................................489

9-5 Dilations..........................................................................490

Practice Quiz 2: Lessons 9-4 and 9-5 .........................497

9-6 Vectors.............................................................................498

9-7 Transformations with Matrices ..................................506

Study Guide and Review ............................................512

Practice Test ..................................................................517

Standardized Test Practice ........................................518

xv

Lesson 9-5, p. 495

Phillip Wallick/CORBIS

Unit 3Unit 3

Chapter Circles 520

10-1 Circles and Circumference...........................................522

10-2 Angles and Arcs ............................................................529

10-3 Arcs and Chords............................................................536

Practice Quiz 1: Lessons 10-1 through 10-3 ..............543

10-4 Inscribed Angles ............................................................544

10-5 Tangents..........................................................................552

Geometry Activity: Inscribed and Circumscribed Triangles...........................................559

10-6 Secants, Tangents, and Angle Measures ....................561

Practice Quiz 2: Lessons 10-4 through 10-6 ..............568

10-7 Special Segments in a Circle ........................................569

10-8 Equations of Circles .....................................................575

Study Guide and Review ............................................581

Practice Test ..................................................................587

Standardized Test Practice ........................................588

Snapshots 531

Standardized Test Practice • Multiple Choice 525, 526, 528, 535, 543, 551, 558,

567, 574, 580, 587, 588

• Short Response/Grid In 528, 535, 543, 551, 558, 589

• Extended Response 589

Constructions 542, 554, 556, 559, 560

Study Organizer 521

Reading and Writing Mathematics • Reading Math Tips 522, 536

• Writing in Math 527, 534, 542, 551, 558, 567, 574, 579

Prerequisite Skills • Getting Started 521

• Getting Ready for the Next Lesson 528, 535, 543, 551,558, 568, 574

xvi

Lesson 10-3, p. 541

Aaron Haupt

• Introduction 591

• Follow-Ups 618, 662, 703

• Culmination 719

xvii

Area and Volume 590

Chapter Areas of Polygons and Circles 592

11-1 Areas of Parallelograms ...............................................595

11-2 Areas of Triangles, Trapezoids, and Rhombi ............601

Practice Quiz 1: Lessons 11-1 and 11-2......................609

11-3 Areas of Regular Polygons and Circles .....................610

11-4 Areas of Irregular Figures............................................617

Practice Quiz 2: Lessons 11-3 and 11-4......................621

11-5 Geometric Probability ..................................................622

Study Guide and Review ............................................628

Practice Test ..................................................................631

Standardized Test Practice ........................................632

Prerequisite Skills• Getting Started 593

• Getting Ready for the Next Lesson600, 609, 616, 621

Study Organizer 593

Reading and WritingMathematics • Prefixes 594

• Reading Math Tips 617

• Writing in Math 600, 608, 616,620, 627

Standardized Test Practice• Multiple Choice 600, 608, 616,

621, 627, 631, 632

• Short Response/Grid In 622, 625, 633

• Extended Response 633

Snapshots 614

Lesson 11-4, p. 617

Paul Barron/CORBIS

Prerequisite Skills• Getting Started 635

• Getting Ready for the Next Lesson642, 648, 654, 659, 665, 670

Study Organizer 635

Reading and WritingMathematics • Reading Math Tips 637, 649, 666

• Writing in Math 641, 648, 653, 658,664, 669, 676

Standardized Test Practice• Multiple Choice 642, 644, 645,

648, 653, 658, 664, 665, 670,676, 683, 684

• Short Response/Grid In 685

• Extended Response 685

Snapshots 653

Unit 4Unit 4

xviii

Chapter Surface Area 634

12-1 Three-Dimensional Figures..........................................636

12-2 Nets and Surface Area ..................................................643

12-3 Surface Areas of Prisms................................................649

12-4 Surface Areas of Cylinders ..........................................655

Practice Quiz 1: Lessons 12-1 through 12-4 ..............659

12-5 Surface Areas of Pyramids...........................................660

12-6 Surface Areas of Cones.................................................666

Practice Quiz 2: Lessons 12-5 and 12-6 .....................670

12-7 Surface Areas of Spheres..............................................671

Geometry Activity: Locus and Spheres.....................677

Study Guide and Review ............................................678

Practice Test ..................................................................683

Standardized Test Practice ........................................684

Lesson 12-5, p. 660

First Image

Unit 4Unit 4

xix

Chapter Volume 686

13-1 Volumes of Prisms and Cylinders ..............................688

Spreadsheet Investigation: Prisms...........................695

13-2 Volumes of Pyramids and Cones................................696

Practice Quiz 1: Lessons 13-1 and 13-2 .....................701

13-3 Volumes of Spheres.......................................................702

13-4 Congruent and Similar Solids .....................................707

Practice Quiz 2: Lessons 13-3 and 13-4 .....................713

13-5 Coordinates in Space ....................................................714

Study Guide and Review ............................................720

Practice Test ..................................................................723

Standardized Test Practice ........................................724

Lesson 13-1, p. 693

Snapshots 705

Standardized Test Practice• Mutiple Choice 694, 701, 706, 713, 719, 723, 724

• Short Response/Grid In 703, 704, 725

• Extended Response 725

Study Organizer 687

Reading and Writing Mathematics • Reading Math Tips 714

• Writing in Math 693, 701, 706, 712, 719

Prerequisite Skills• Getting Started 687

• Getting Ready for the Next Lesson 694, 701, 706, 713

CORBIS

Student Handbook

xx

Skills

Prerequisite Skills ..........................................................728

Extra Practice .................................................................754

Mixed Problem Solving and Proof .............................782

Preparing for Standardized Tests................................795

Reference

Postulates, Theorems, and Corollaries.........................R1

English-Spanish Glossary ..............................................R9

Selected Answers ..........................................................R29

Photo Credits .................................................................R77

Index ...............................................................................R79

Symbols and Formulas ......................Inside Back Cover

Brandon D. Cole