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
