CHAPTER
1Basics of Geometry
CHAPTER STUDY GUIDE 2
1.1 Patterns and Inductive Reasoning 3
1.2 Points, Lines, and Planes 10
1.3 Segments and Their Measures 17QUIZ 1, 25
1.4 Angles and Their Measures 26
1.5 Segment and Angle Bisectors 34
� CONCEPT ACTIVITY: Folding Bisectors, 33QUIZ 2, 42
1.6 Angle Pair Relationships 44
� TECHNOLOGY ACTIVITY: Angles and Intersecting Lines, 43
1.7 Introduction to Perimeter, Circumference, and Area 51QUIZ 3, 58
ASSESSMENT
Skill Review, 2Quizzes, 25, 42, 58Test Preparation Questions, 9, 16, 24, 31,41, 50, 57
Chapter Summary, Review, and Test, 59Chapter Standardized Test, 64Project, Chapter 1, 66
APPLICATIONHIGHLIGHTS
Airport Runways 1, 32Bacteria Growth 8Two-Point Perspective 15Long-Distance Rates 23Playing Darts 31Kite Design 37Strike Zone 40Paper Airplanes 41Bridges 49Millennium Dome 56
MATH & HISTORY
Geometric Constructions 25
INTERNETCONNECTIONS
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Application Links1, 25, 49, 56
Student Help7, 12, 22, 28, 39, 40, 41, 45,56
Career Links8, 30
Extra Challenge9, 16, 24, 32, 41
vi Contents
Basics of Geometry
�READING, WRITING, ANDNOTETAKING
Reading 2, 10, 11, 17, 18, 19, 26, 27, 28,34, 36, 44, 46Writing 41, 50Notetaking 2, 17–20, 27, 35, 51, 53, 59Vocabulary 2, 6, 13, 21, 29, 38, 47, 55, 60
Contents vii
CHAPTER
2Reasoning and Proof
CHAPTER STUDY GUIDE 70
2.1 Conditional Statements 71
2.2 Definitions and Biconditional Statements 79
2.3 Deductive Reasoning 87
� CONCEPT ACTIVITY: Logic Puzzle, 86QUIZ 1, 95
2.4 Reasoning with Properties from Algebra 96
2.5 Proving Statements about Segments 102
2.6 Proving Statements about Angles 109
� CONCEPT ACTIVITY: Investigating Complementary Angles, 108QUIZ 2, 116
ASSESSMENT
Skill Review, 70Quizzes, 95, 116Test Preparation Questions, 78, 85, 94,101, 107, 115Chapter Summary, Review, and Test, 117Chapter Standardized Test, 122Algebra Review, 124
APPLICATIONHIGHLIGHTS
Robotics 69, 93Advertising 77Research Buggy 77Winds at Sea 84Zoology 90Fitness 97Auto Racing 98Wind-Chill Factor 99Pay Raises 100Optical Illusion 106Wall Trim 115
MATH & HISTORY
Recreational Logic Puzzles 95
INTERNETCONNECTIONS
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Application Links69, 84, 95
Student Help72, 76, 88, 93, 97, 114
Career Links77, 90, 106
Extra Challenge78, 85, 94, 101, 107
Reasoning and Proof
�READING, WRITING, ANDNOTETAKING
Reading 71, 72, 74, 79, 80, 87, 88, 103Writing 76, 77, 84, 91, 93, 94, 101, 115Notetaking 70, 73, 96, 98, 102, 109–112,117Vocabulary 70, 75, 82, 91, 99, 104,112, 118
CHAPTER
3Perpendicular andParallel Lines
CHAPTER STUDY GUIDE 128
3.1 Lines and Angles 129
3.2 Proof and Perpendicular Lines 136
� CONCEPT ACTIVITY: Forming a Flow Proof, 135
3.3 Parallel Lines and Transversals 143
� TECHNOLOGY ACTIVITY: Parallel Lines and Angles, 142QUIZ 1, 149
3.4 Proving Lines are Parallel 150
3.5 Using Properties of Parallel Lines 157QUIZ 2, 164
3.6 Parallel Lines in the Coordinate Plane 165
3.7 Perpendicular Lines in the Coordinate Plane 172QUIZ 3, 178
ASSESSMENT
Skill Review, 128Quizzes, 149, 164, 178Test Preparation Questions, 134, 141,148,156, 163, 171, 177Chapter Summary, Review, and Test, 179Chapter Standardized Test, 184Cumulative Practice, Chapters 1–3, 186Project, Chapters 2 and 3, 188
APPLICATIONHIGHLIGHTS
Sailing 127, 152Escalators 133Circuit Boards 140Botany 144Earth’s Circumference 145Rainbows 148Snow Making 156Zip Line 170Ray Tracing 174Needlepoint 176Sculpture 177
MATH & HISTORY
Measuring Earth’sCircumference 164
INTERNETCONNECTIONS
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Application Links127, 145, 154, 163, 164
Student Help131, 140, 147, 152, 161, 167,176
Career Links144, 170, 174
Extra Challenge134, 141, 148, 156, 177
viii Contents
Perpendicular and Parallel Lines
�READING, WRITING, ANDNOTETAKING
Reading 128, 129, 131, 165, 167, 174Writing 134, 148, 155, 160, 163, 177, 178Notetaking 128, 130, 137–138, 143, 150,157, 166, 172, 179Vocabulary 128, 132, 138, 146, 153, 168,175, 180
Contents ix
CHAPTER
4Congruent Triangles
CHAPTER STUDY GUIDE 192
4.1 Triangles and Angles 194
� CONCEPT ACTIVITY: Investigating Angles of Triangles, 193
4.2 Congruence and Triangles 202QUIZ 1, 210
4.3 Proving Triangles are Congruent: SSS and SAS 212
� CONCEPT ACTIVITY: Investigating Congruent Triangles, 211
4.4 Proving Triangles are Congruent: ASA and AAS 220QUIZ 2, 227
� TECHNOLOGY ACTIVITY: Investigating Triangles and Congruence, 228
4.5 Using Congruent Triangles 229
4.6 Isosceles, Equilateral, and Right Triangles 236
4.7 Triangles and Coordinate Proof 243QUIZ 3, 250
ASSESSMENT
Skill Review, 192Quizzes, 210, 227, 250Test Preparation Questions, 201, 209,219, 226, 235, 242, 249Chapter Summary, Review, and Test, 251Chapter Standardized Test, 256Algebra Review, 258
APPLICATIONHIGHLIGHTS
Bridges 191, 234Weaving 195Wing Deflectors 200Stamps 204Crop Circles 207Origami 208Structural Support 215Astronomy 222Orienteering 225Color Wheel 241
MATH & HISTORY
Triangles in Architecture210
INTERNETCONNECTIONS
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Application Links191, 210, 241
Student Help199, 203, 217, 230, 237, 243,245
Career Links200, 234
Extra Challenge201, 209, 219, 226, 235, 242,249
Congruent Triangles
�READING, WRITING, ANDNOTETAKING
Reading 192, 195, 196, 202, 229, 236Writing 209, 218, 226, 250Notetaking 192, 194–197, 203, 205,212–213, 220, 236–238, 251Vocabulary 192, 198, 205, 216, 223, 239,246, 252
CHAPTER
5Properties of Triangles
CHAPTER STUDY GUIDE 262
5.1 Perpendiculars and Bisectors 264
� CONCEPT ACTIVITY: Investigating Perpendicular Bisectors, 263
5.2 Bisectors of a Triangle 272
5.3 Medians and Altitudes of a Triangle 279QUIZ 1, 285
� TECHNOLOGY ACTIVITY: Investigating Concurrent Lines, 286
5.4 Midsegment Theorem 287
5.5 Inequalities in One Triangle 295
� TECHNOLOGY ACTIVITY: Side Lengths and Angle Measures, 294
5.6 Indirect Proof and Inequalities in Two Triangles 302QUIZ 2, 308
ASSESSMENT
Skill Review, 262Quizzes, 285, 308Test Preparation Questions, 271, 278,284,292, 301, 307Chapter Summary, Review, and Test, 309Chapter Standardized Test, 314Project, Chapters 4 and 5, 316
APPLICATIONHIGHLIGHTS
Goalkeeping 261, 270Roof Truss 267Early Aircraft 269Mushroom Rings 277Center of Population 280Electrocardiograph 283Fractals 291Surveying Land 298Kitchen Triangle 299Hiking 308
MATH & HISTORY
Optimization 285
INTERNETCONNECTIONS
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Application Links261, 291
Student Help273, 280, 291, 300, 306
Career Links267, 283, 304
Extra Challenge271, 278, 284, 293, 301, 307
x Contents
Properties of Triangles
�READING, WRITING, ANDNOTETAKING
Reading 262, 264, 266, 272, 274, 279,287, 303Writing 271, 277, 284, 292, 307Notetaking 262, 265–266, 273–274, 279,281, 288, 295–297, 302–303, 309Vocabulary 262, 267, 275, 282, 290, 298,305, 310
Contents xi
CHAPTER
6Quadrilaterals
CHAPTER STUDY GUIDE 320
6.1 Polygons 322
� CONCEPT ACTIVITY: Classifying Shapes, 321
6.2 Properties of Parallelograms 330
� TECHNOLOGY ACTIVITY: Investigating Parallelograms, 329
6.3 Proving Quadrilaterals are Parallelograms 338QUIZ 1, 346
6.4 Rhombuses, Rectangles, and Squares 347
6.5 Trapezoids and Kites 356QUIZ 2, 363
6.6 Special Quadrilaterals 364
6.7 Areas of Triangles and Quadrilaterals 372
� CONCEPT ACTIVITY: Areas of Quadrilaterals, 371QUIZ 3, 380
ASSESSMENT
Skill Review, 320Quizzes, 346, 363, 380Test Preparation Questions, 328, 337,345, 355, 362, 370, 379Chapter Summary, Review, and Test, 381Chapter Standardized Test, 386Cumulative Practice, Chapters 1–6, 388Algebra Review, 390
APPLICATIONHIGHLIGHTS
Scissors Lift 319, 336Traffic Signs 326Plant Shapes 327Furniture Design 333Hinged Box 339Changing Gears 343Carpentry 350Layer Cake 361Gem Cutting 369Energy Conservation 377
MATH & HISTORY
History of Finding Area 346
INTERNETCONNECTIONS
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Application Links319, 346, 377
Student Help335, 341, 344, 349, 357, 369
Career Links333, 361, 369
Extra Challenge328, 337, 345, 355, 362, 379
Quadrilaterals
�READING, WRITING, ANDNOTETAKING
Reading 320, 322, 323, 324, 330, 347, 356,364, 372Writing 328, 335–337, 355, 370, 379Notetaking 320, 324, 330, 338, 340,348–349, 356–358, 365, 372, 374, 381Vocabulary 320, 325, 333, 351, 359,376, 382
CHAPTER
7Transformations
CHAPTER STUDY GUIDE 394
7.1 Rigid Motion in a Plane 396
� CONCEPT ACTIVITY: Motion in a Plane, 395
7.2 Reflections 404
� CONCEPT ACTIVITY: Reflections in the Plane, 403
7.3 Rotations 412
� TECHNOLOGY ACTIVITY: Investigating Double Reflections, 411QUIZ 1, 420
7.4 Translations and Vectors 421
7.5 Glide Reflections and Compositions 430
� CONCEPT ACTIVITY: Multiple Transformations, 429
7.6 Frieze Patterns 437QUIZ 2, 444
ASSESSMENT
Skill Review, 394Quizzes, 420, 444Test Preparation Questions, 402, 410,419, 428, 436, 443Chapter Summary, Review, and Test, 445Chapter Standardized Test, 450Project, Chapters 6 and 7, 452
APPLICATIONHIGHLIGHTS
Architecture 393, 435Construction 398Machine Embroidery 401Kaleidoscopes 406Logo Design 415Wheel Hubs 418Pentominoes 432Stenciling 435Pet Collars 441Celtic Knots 443
MATH & HISTORY
History of DecorativePatterns 420
INTERNETCONNECTIONS
www.mcdougallittell.com
Application Links393, 406, 418, 420
Student Help400, 408, 414, 424, 426, 434,443
Career Links409, 415, 435
Extra Challenge402, 410, 419, 428, 436
xii Contents
Transformations
�READING, WRITING, ANDNOTETAKING
Reading 394, 396, 397, 404, 405, 412, 415,421, 423, 430, 438Writing 401, 419, 434, 442–443Notetaking 394, 404, 412, 414, 421, 431,438, 445Vocabulary 394, 399, 407, 416, 425, 433,440, 446
Contents xiii
CHAPTER
8Similarity
CHAPTER STUDY GUIDE 456
8.1 Ratio and Proportion 457
8.2 Problem Solving in Geometry with Proportions 465
8.3 Similar Polygons 473
� CONCEPT ACTIVITY: Making Conjectures about Similarity, 472QUIZ 1, 479
8.4 Similar Triangles 480
8.5 Proving Triangles are Similar 488QUIZ 2, 496
8.6 Proportions and Similar Triangles 498
� TECHNOLOGY ACTIVITY: Investigating Proportional Segments, 497
8.7 Dilations 506QUIZ 3, 513
� TECHNOLOGY ACTIVITY: Exploring Dilations, 514
ASSESSMENT
Skill Review, 456Quizzes, 479, 496, 513Test Preparation Questions, 464, 471,478,487, 495, 505, 512Chapter Summary, Review, and Test, 515Chapter Standardized Test, 520Algebra Review, 522
APPLICATIONHIGHLIGHTS
Scale Drawing 455, 490Baseball Sculpture 463Paper Sizes 466Model Building 467Ramp Design 470Television Screens 477Aerial Photography 482Human Vision 487Pantograph 490Indirect Distances 494Shadow Puppets 508
MATH & HISTORY
Golden Rectangle 496
INTERNETCONNECTIONS
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Application Links455, 462, 469, 496
Student Help463, 466, 477, 482, 485, 491,504, 511
Career Links482, 503, 512
Extra Challenge471, 478, 487, 495
Similarity
�READING, WRITING, ANDNOTETAKING
Reading 456, 457, 459, 473, 506Writing 470, 505, 512Notetaking 456, 459, 465, 475, 481, 488,498–499, 515Vocabulary 456, 461, 468, 475, 483, 492,502, 509, 516
CHAPTER
9Right Trianglesand Trigonometry
CHAPTER STUDY GUIDE 526
9.1 Similar Right Triangles 527
9.2 The Pythagorean Theorem 535
9.3 The Converse of the Pythagorean Theorem 543
� TECHNOLOGY ACTIVITY: Investigating Sides and Angles of Triangles, 542QUIZ 1, 549
9.4 Special Right Triangles 551
� CONCEPT ACTIVITY: Investigating Special Right Triangles, 550
9.5 Trigonometric Ratios 558QUIZ 2, 566
9.6 Solving Right Triangles 567
9.7 Vectors 573QUIZ 3, 580
ASSESSMENT
Skill Review, 526Quizzes, 549, 566, 580Test Preparation Questions, 534, 541,548, 556, 565, 572, 579Chapter Summary, Review, and Test, 581Chapter Standardized Test, 586Cumulative Practice, Chapters 1–9, 588Project, Chapters 8 and 9, 590
APPLICATIONHIGHLIGHTS
Support Beam 525, 537Monorail 530Rock Climbing 532Construction 545Moon Craters 564Parade Balloon 565Space Shuttle 569Tug of War 577Skydiving 578Bumper Cars 579
MATH & HISTORY
Pythagorean TheoremProofs 557
INTERNETCONNECTIONS
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Application Links525, 557
Student Help532, 540, 547, 552, 559, 569
Career Links540, 561, 569
Extra Challenge534, 541, 548, 556, 565, 572,579
xiv Contents
Right Trianglesand Trigonometry
�READING, WRITING, ANDNOTETAKING
Reading 530, 558, 568, 573, 575Writing 534, 541, 564, 571–572, 579Notetaking 526, 527, 529, 535, 543–544,551, 558, 575, 581Vocabulary 526, 531, 538, 545, 554, 562,570, 576, 582
Contents xv
CHAPTER
10Circles
CHAPTER STUDY GUIDE 594
Tangents to Circles 595
Arcs and Chords 603
Inscribed Angles 613
� CONCEPT ACTIVITY: Investigating Inscribed Angles, 612QUIZ 1, 620
Other Angle Relationships in Circles 621
Segment Lengths in Circles 629
� TECHNOLOGY ACTIVITY: Investigating Segment Lengths, 628QUIZ 2, 635
Equations of Circles 636
Locus 642
� TECHNOLOGY ACTIVITY: Investigating Points Equidistantfrom a Point and a Line, 641QUIZ 3, 648
ASSESSMENT
Skill Review, 594Quizzes, 620, 635, 648Test Preparation Questions, 602, 611,619, 627, 634, 640, 647Chapter Summary, Review, and Test, 649Chapter Standardized Test, 654Algebra Review, 656
10.7
10.6
10.5
10.4
10.3
10.2
10.1
APPLICATIONHIGHLIGHTS
Fireworks 593, 625Pick Ax 606Time Zone Wheel 609Avalanche Rescue Beacon
609Theater Design 614Carpenter’s Square 619Aquarium Tank 631Global Positioning System
634Cellular Phones 639Earthquake Epicenter 644
MATH & HISTORY
History of Timekeeping 648
INTERNETCONNECTIONS
www.mcdougallittell.com
Application Links593, 625, 631, 634, 639, 648
Student Help596, 610, 622, 633
Career Links609, 644
Extra Challenge602, 611, 619, 627, 634, 640
Circles
�READING, WRITING, ANDNOTETAKING
Reading 595, 596, 603, 622, 630, 636, 644Writing 602, 611, 634Notetaking 594, 597–598, 604–606,613–615, 621–622, 629–630, 642, 649Vocabulary 594, 599, 607, 616, 632, 638,645, 650
CHAPTER
11Area of Polygonsand Circles
CHAPTER STUDY GUIDE 660
Angle Measures in Polygons 661
Areas of Regular Polygons 669
Perimeters and Areas of Similar Figures 677
� CONCEPT ACTIVITY: Area Relationships in Similar Figures, 676QUIZ 1, 682
Circumference and Arc Length 683
� TECHNOLOGY ACTIVITY: Perimeters of Regular Polygons, 690
Areas of Circles and Sectors 691
Geometric Probability 699QUIZ 2, 705
� TECHNOLOGY ACTIVITY: Investigating Experimental Probability, 706
ASSESSMENT
Skill Review, 660Quizzes, 682, 705Test Preparation Questions, 668, 675,681, 689, 698, 704Chapter Summary, Review, and Test, 707Chapter Standardized Test, 712Project, Chapters 10 and 11, 714
11.6
11.5
11.4
11.3
11.2
11.1
APPLICATIONHIGHLIGHTS
Basaltic Columns 659, 673Foucault Pendulums 671Tiling 674Fort Jefferson 680Track 685Boomerangs 694Viking Longships 697Ship Salvage 703Archery Target 703Balloon Race 704
MATH & HISTORY
Approximating Pi 682
INTERNETCONNECTIONS
www.mcdougallittell.com
Application Links659, 671, 678, 682, 697
Student Help662, 674, 680, 684, 692, 700
Career Links674, 703
Extra Challenge675, 681, 689, 698, 704
xvi Contents
Area of Polygonsand Circles
�READING, WRITING, ANDNOTETAKING
Reading 661, 663, 669, 670, 677, 683,684, 691, 692Writing 666, 673, 681, 697, 704Notetaking 660, 662–663, 669–670,677, 683, 691–692, 699, 707Vocabulary 660, 665, 672, 679, 686,695, 701, 708
Contents xvii
CHAPTER
12Surface Areaand Volume
CHAPTER STUDY GUIDE 718
Exploring Solids 719
Surface Area of Prisms and Cylinders 728
� CONCEPT ACTIVITY: Investigating Surface Area, 727
Surface Area of Pyramids and Cones 735QUIZ 1, 742
Volume of Prisms and Cylinders 743
� TECHNOLOGY ACTIVITY: Minimizing Surface Area, 750
Volume of Pyramids and Cones 752
� CONCEPT ACTIVITY: Investigating Volume, 751QUIZ 2, 758
Surface Area and Volume of Spheres 759
Similar Solids 766QUIZ 3, 772
ASSESSMENT
Skill Review, 718Quizzes, 742, 758, 772Test Preparation Questions, 726, 734,741, 749, 757, 765, 771Chapter Summary, Review, and Test, 773Chapter Standardized Test, 778Cumulative Practice, Chapters 1–12, 780
12.7
12.6
12.5
12.4
12.3
12.2
12.1
APPLICATIONHIGHLIGHTS
Spherical Buildings 717,764
Soccer Ball 722Wax Cylinder Records 733Pyramids 740Candles 748Nautical Prism 754Automatic Pet Feeder 756Baseball 760Ball Bearings 761Model Car 770
MATH & HISTORY
History of Containers 742
INTERNETCONNECTIONS
www.mcdougallittell.com
Application Links717, 722, 742, 763
Student Help725, 730, 739, 747, 756, 760,764
Career Links725, 757, 768
Extra Challenge726, 734, 741, 749, 765, 771
Surface Areaand Volume
�READING, WRITING, ANDNOTETAKING
Reading 719, 720, 721, 728, 730, 735, 737,753, 759, 760, 766Writing 734, 757Notetaking 718, 721, 729–730, 736–737,743–744, 752, 759, 761, 767, 773Vocabulary 718, 723, 731, 738, 746, 755,762, 769, 774
SKILLS REVIEW HANDBOOK 783
EXTRA PRACTICE FOR CHAPTERS 1–12 803
POSTULATES AND THEOREMS 827
ADDITIONAL PROOFS 833
SYMBOLS, FORMULAS, AND TABLES 841
MIXED PROBLEM SOLVING 846
APPENDICES 858
GLOSSARY 876
ENGLISH-TO-SPANISH GLOSSARY 888
INDEX 901
SELECTED ANSWERS SA1
xviii Contents
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