1 Check Your Readiness 2 Check Skills You ll Need 4, 10, 16, 23, 31, 36, 44, 53, 61 Quick Check 4, 5, 6, 10, 11, 12, 17, 19, 23, 24, 25, 32, 33, 36, 37, 38, 39, 44, 45, 46, 47, 54, 55, 62, 63, 64 Checkpoint Quiz 28, 59 New 4, 10, 16, 23, 31, 36, 44 Tip 10, 17, 18, 24, 26, 31, 34, 36, 53, 61, 62, 63 Builder 29 Review 71 Video Tutor Help 37, 39, 63 Active Math 45, 54, 61, 64 Homework Help 8, 14, 23, 26, 34, 41, 48, 56, 67 Lesson Quizzes 9, 15, 21, 27, 35, 41, 49, 59, 67 Quiz 71 Chapter Test 74 Geometry at Work 50 Tools of Geometry Check Your Readiness............................. 2 1-1 Patterns and Inductive Reasoning......................... 4 1-2 Drawings, Nets, and Other Models....................... 10 1-3 Points, Lines, and Planes............................... 16 1-4 Segments, Rays, Parallel Lines and Planes................. 23 Builder Geometry, 29 Checkpoint Quiz 1................................ 28 1-5 Measuring Segments.................................. 31 Algebra 1 Review: Solving Linear Equations, 30 1-6 Measuring Angles.................................... 36 1-7 Basic Constructions................................... 44 Activity Lab Hands-On: Compass Designs, 43 Activity Lab Technology: Exploring Constructions, 51 1-8 The Coordinate Plane................................. 53 Activity Lab Distance in the Coordinate Plane, 52 Guided Problem Solving Understanding Word Problems, 60 Checkpoint Quiz 2................................ 59 1-9 Perimeter, Circumference, and Area...................... 61 Activity Lab Technology: Comparing Perimeters and Areas, 69 Activity Lab Data Analysis: Linear Regression, 76 Test-Taking Strategies: Writing Gridded Responses, 70 Chapter Review, 71 Chapter Test, 74 Standardized Test Prep: Reading Comprehension, 75 T8 viii
2 Reasoning and Proof Check Your Readiness 78 Check Skills You ll Need 80, 87, 94, 103, 110 Quick Check 80, 81, 82, 87, 88, 89, 94, 95, 96, 104, 105, 111, 112 Checkpoint Quiz 100 New 80, 87, 94, 103, 110 Tip 87, 92, 95, 96 Review 117 Check Your Readiness............................ 78 2-1 Conditional Statements................................ 80 2-2 Biconditionals and Definitions........................... 87 2-3 Deductive Reasoning.................................. 94 Activity Lab: Mathematical Systems, 101 Checkpoint Quiz 1............................... 100 2-4 Reasoning in Algebra................................. 103 Activity Lab Hands-On: Paper-Folding Constructions, 102 Guided Problem Solving Understanding Math Problems, 109 2-5 Proving Angles Congruent............................. 110 Activity Lab Applying Reasoning, 122 Active Math 80, 89 Homework Help 85, 91, 97, 106, 113 Lesson Quizzes 85, 93, 99, 107, 115 Quiz 117 Chapter Test 120 A Point in Time 100 Test-Taking Strategies: Writing Short Responses, 116 Chapter Review, 117 Chapter Test, 120 Standardized Test Prep: Cumulative Review, 121 ix T9
3 Check Your Readiness 124 Check Skills You ll Need 127, 134, 141, 147, 157, 166, 174, 181 Quick Check 127, 128, 129, 130, 135, 136, 137, 142, 148, 149, 150, 157, 158, 159, 160, 166, 167, 168, 174, 175, 176, 177, 181, 182, 183 Checkpoint Quiz 153, 180 New 127, 134, 147, 157, 166 Tip 128, 129, 149, 158, 159, 166, 167, 176 Review 189 Video Tutor Help 127, 148, 159 Active Math 149, 160, 182 Homework Help 132, 138, 144, 152, 162, 170, 178, 185 Lesson Quizzes 133, 139, 143, 153, 163, 171, 179, 185 Quiz 189 Chapter Test 192 Parallel and Perpendicular Lines Check Your Readiness........................... 124 3-1 Properties of Parallel Lines............................. 127 Activity Lab Technology: Parallel Lines and Related Angles, 126 3-2 Proving Lines Parallel................................. 134 3-3 Parallel and Perpendicular Lines........................ 141 Guided Problem Solving Understanding Proof Problems, 145 3-4 Parallel Lines and the Triangle Angle-Sum Theorem........ 147 Activity Lab Hands-On: Angle Dynamics, 146 Activity Lab Exploring Spherical Geometry, 154 Checkpoint Quiz 1............................... 153 3-5 The Polygon Angle-Sum Theorems...................... 157 Activity Lab Technology: Exterior Angles of Polygons, 156 3-6 Lines in the Coordinate Plane.......................... 166 Algebra 1 Review: Slope, 165 Activity Lab Technology: Solving Linear Equations With Graphs and Tables, 172 3-7 Slopes of Parallel and Perpendicular Lines................ 174 Checkpoint Quiz 2............................... 180 3-8 Constructing Parallel and Perpendicular Lines............. 181 Activity Lab Technology: Using Tables and Lists, 187 Activity Lab Applying Parallel Lines, 194 Test-Taking Strategies: Writing Extended Responses, 188 Chapter Review, 189 Chapter Test, 192 Standardized Test Prep: Reading Comprehension, 193 T10 x
Chapter 4 Check Your Readiness 196 Check Skills You ll Need 198, 205, 213, 221, 228, 235, 241 Quick Check 198, 199, 200, 206, 207, 213, 214, 215, 221, 222, 229, 230, 236, 237, 241, 242, 243 Checkpoint Quiz 219, 240 New 198, 221, 228, 235 Tip 206, 228, 230, 241 Builder 212 Review 249 Video Tutor Help 207, 215 Active Math 207, 230, 236 Homework Help 202, 209, 217, 223, 231, 238, 244 Lesson Quizzes 201, 211, 219, 225, 233, 239, 245 Quiz 249 Chapter Test 252 Geometry at Work 203 Congruent Triangles Check Your Readiness........................... 196 4-1 Congruent Figures................................... 198 4-2 Triangle Congruence by SSS and SAS.................... 205 Activity Lab Hands-On: Building Congruent Triangles, 204 Builder High-Use Academic Words, 212 4-3 Triangle Congruence by ASA and AAS................... 213 Activity Lab Technology: Exploring AAA and SSA, 220 Checkpoint Quiz 1............................... 219 4-4 Using Congruent Triangles: CPCTC...................... 221 Guided Problem Solving Analyzing Errors, 226 4-5 Isosceles and Equilateral Triangles...................... 228 Activity Lab Hands-On: Paper-Folding Conjectures, 227 4-6 Congruence in Right Triangles.......................... 235 Algebra 1 Review: Systems of Linear Equations, 234 Checkpoint Quiz 2............................... 240 4-7 Using Corresponding Parts of Congruent Triangles......... 241 Extension: Writing Flow Proofs, 247 Activity Lab Data Analysis: Probability, 254 Test-Taking Strategies: Interpreting Data, 248 Chapter Review, 249 Chapter Test, 252 Standardized Test Prep: Cumulative Review, 253 xi T11
5 Check Your Readiness 256 Check Skills You ll Need 259, 265, 272, 280, 289 Quick Check 260, 261, 266, 267, 273, 274, 275, 280, 281, 282, 283, 290, 291, 292 Checkpoint Quiz 279 New 259, 265, 272, 280 Tip 260, 273, 280 Review 297 Active Math 266, 275, 292 Homework Help 263, 268, 277, 284, 294 Lesson Quizzes 263, 269, 279, 285, 295 Quiz 297 Chapter Test 300 Geometry at Work 286 Relationships Within Triangles Check Your Readiness........................... 256 5-1 Midsegments of Triangles............................. 259 Activity Lab Technology: Investigating Midsegments, 258 5-2 Bisectors in Triangles................................. 265 5-3 Concurrent Lines, Medians, and Altitudes................ 272 Activity Lab Technology: Special Segments in Triangles, 271 Checkpoint Quiz 1............................... 279 5-4 Inverses, Contrapositives, and Indirect Reasoning.......... 280 Guided Problem Solving Understanding Proof Problems, 287 5-5 Inequalities in Triangles............................... 289 Algebra 1 Review: Solving Inequalities, 288 Activity Lab Applying Theorems About Triangles, 302 Test-Taking Strategies: Using a Variable, 296 Chapter Review, 297 Chapter Test, 300 Standardized Test Prep: Reading Comprehension, 301 T12 xii
6 Check Your Readiness 304 Check Skills You ll Need 306, 312, 321, 329, 336, 343, 348 Quick Check 307, 308, 313, 314, 315, 323, 324, 330, 331, 332, 337, 338, 343, 344, 349 Checkpoint Quiz 327, 347 New 306, 312, 336, 348 Tip 307, 312, 329 Review 357 Active Math 307, 323, 331 Homework Help 310, 317, 325, 333, 339, 345, 351 Lesson Quizzes 311, 317, 327, 335, 341, 345, 353 Quiz 357 Chapter Test 360 A Point in Time 347 Quadrilaterals Check Your Readiness........................... 304 6-1 Classifying Quadrilaterals............................. 306 6-2 Properties of Parallelograms........................... 312 Guided Problem Solving Understanding Proof Problems, 319 6-3 Proving That a Quadrilateral is a Parallelogram............ 321 Activity Lab Hands-On: Geo-Models, 320 Checkpoint Quiz 1............................... 327 6-4 Special Parallelograms................................ 329 Activity Lab Technology: Diagonals of Parallelograms, 328 6-5 Trapezoids and Kites.................................. 336 Activity Lab Technology: Quadrilaterals in Quadrilaterals, 342 6-6 Placing Figures in the Coordinate Plane.................. 343 Checkpoint Quiz 2............................... 347 6-7 Proofs Using Coordinate Geometry...................... 348 Algebra 1 Review: Quadratics, 354 Activity Lab Data Analysis: Interpreting Data, 362 Test-Taking Strategies: Drawing a Diagram, 356 Chapter Review, 357 Chapter Test, 360 Standardized Test Prep: Cumulative Review, 361 xiii T13
7 Similarity Check Your Readiness 364 Check Skills You ll Need 366, 373, 382, 391, 398 Quick Check 366, 367, 368, 373, 374, 375, 383, 384, 385, 392, 393, 399, 400 Checkpoint Quiz 379, 404 New 366, 373, 382, 391 Tip 366, 367, 392, 394 Builder 389 Review 407 Active Math 374, 393 Homework Help 369, 377, 387, 395, 402 Lesson Quizzes 369, 379, 387, 395, 403 Quiz 407 Chapter Test 410 A Point in Time 371 Check Your Readiness........................... 364 7-1 Ratios and Proportions................................ 366 7-2 Similar Polygons..................................... 373 Algebra 1 Review: Solving Quadratic Equations, 372 Extension: Fractals, 380 Checkpoint Quiz 1............................... 379 7-3 Proving Triangles Similar.............................. 382 Builder Abbreviations and Symbols, 389 7-4 Similarity in Right Triangles............................ 391 Algebra 1 Review: Simplifying Radicals, 390 7-5 Proportions in Triangles............................... 398 Activity Lab Technology: Exploring Proportions in Triangles, 397 Guided Problem Solving Understanding Word Problems, 405 Checkpoint Quiz 2............................... 404 Activity Lab Data Analysis: Accuracy and Precision in Measuring, 412 Test-Taking Strategies: Testing Multiple Choices, 406 Chapter Review, 407 Chapter Test, 410 Standardized Test Prep: Reading Comprehension, 411 T14 xiv
8 Check Your Readiness 414 Check Skills You ll Need 417, 425, 432, 439, 445, 452 Quick Check 418, 419, 425, 426, 427, 433, 434, 439, 440, 445, 446, 453, 454, 455 Checkpoint Quiz 430, 450 New 417, 432, 439, 445, 452 Tip 417, 432 Review 461 Active Math 419, 434, 440, 454 Homework Help 421, 429, 435, 442, 447, 458 Lesson Quizzes 423, 429, 437, 443, 449, 459 Quiz 461 Chapter Test 464 Right Triangles and Trigonometry Check Your Readiness........................... 414 8-1 The Pythagorean Theorem and Its Converse.............. 417 Activity Lab Hands-On: The Pythagorean Theorem, 416 Guided Problem Solving Understanding Word Problems, 424 8-2 Special Right Triangles................................ 425 Checkpoint Quiz 1............................... 430 8-3 The Tangent Ratio.................................... 432 Activity Lab Hands-On: The Staff and Stadiascope, 431 8-4 Sine and Cosine Ratios................................ 439 Activity Lab Technology: Exploring Trigonometric Ratios, 438 8-5 Angles of Elevation and Depression..................... 445 Activity Lab Hands-On: Measuring From Afar, 444 Guided Problem Solving Understanding Word Problems, 451 Checkpoint Quiz 2............................... 450 8-6 Vectors............................................. 452 Activity Lab Applying the Pythagorean Theorem, 466 Test-Taking Strategies: Eliminating Answers, 460 Chapter Review, 461 Chapter Test, 464 Standardized Test Prep: Cumulative Review, 465 xv T15
9 Transformations Check Your Readiness 468 Check Skills You ll Need 470, 478, 483, 492, 498, 506, 515 Quick Check 470, 471, 472, 479, 484, 485, 492, 493, 499, 506, 507, 508, 509, 515, 516, 517 Checkpoint Quiz 488, 521 New 470, 478, 483, 492, 498, 506, 515 Tip 470, 471, 484, 493, 515 Builder 497 Review 523 Active Math 479 Homework Help 475, 480, 487, 495, 502, 510, 519 Lesson Quizzes 475, 481, 487, 495, 503, 511, 519 Quiz 523 Chapter Test 526 A Point in Time 521 Check Your Readiness........................... 468 9-1 Translations......................................... 470 9-2 Reflections.......................................... 478 Activity Lab Hands-On: Paper Folding and Reflections, 477 9-3 Rotations........................................... 483 Guided Problem Solving Understanding Math Problems, 489 Activity Lab Hands-On: Tracing-Paper Transformations, 490 Checkpoint Quiz 1............................... 488 9-4 Symmetry.......................................... 492 Builder Extend and Generalize, 497 9-5 Dilations............................................ 498 Extension: Transformations Using Vectors and Matrices, 504 9-6 Compositions of Reflections........................... 506 Activity Lab Technology: Kaleidoscopes, 513 9-7 Tessellations........................................ 515 Activity Lab Hands-On: Frieze Patterns, 514 Checkpoint Quiz 2............................... 521 Activity Lab Applying Translations and Rotations, 528 Test-Taking Strategies: Answering the Question Asked, 522 Chapter Review, 523 Chapter Test, 526 Standardized Test Prep: Reading Comprehension, 527 T16 xvi
10 Check Your Readiness 530 Check Skills You ll Need 534, 540, 546, 553, 559, 566, 575, 582 Quick Check 535, 536, 540, 541, 542, 546, 547, 554, 555, 559, 560, 561, 567, 568, 569, 576, 577, 582, 583, 584 Checkpoint Quiz 551, 580 New 534, 540, 546, 566, 575, 582 Tip 534, 540, 546, 559, 566, 582 Review 589 Video Tutor Help 535, 542 Active Math 535, 555, 583 Homework Help 537, 543, 549, 556, 562, 570, 578, 585 Lesson Quizzes 539, 543, 549, 557, 563, 573, 579, 587 Quiz 589 Chapter Test 592 A Point in Time 545 Geometry at Work 564 Area Check Your Readiness........................... 530 10-1 Areas of Parallelograms and Triangles................... 534 Activity Lab Hands-On: Transforming to Find Area, 532 10-2 Areas of Trapezoids, Rhombuses, and Kites............... 540 10-3 Areas of Regular Polygons............................. 546 Guided Problem Solving Understanding Word Problems, 552 Checkpoint Quiz 1............................... 551 10-4 Perimeters and Areas of Similar Figures.................. 553 10-5 Trigonometry and Area............................... 559 Extension: Laws of Sines and Cosines, 565 10-6 Circles and Arcs...................................... 566 10-7 Areas of Circles and Sectors............................ 575 Algebra 1 Review: Dimensional Analysis, 574 Activity Lab Technology: Exploring Area and Circumference, 581 Checkpoint Quiz 2............................... 580 10-8 Geometric Probability................................. 582 Activity Lab Data Analysis: Misleading Graphs, 594 Test-Taking Strategies: Finding Multiple Correct Answers, 588 Chapter Review, 589 Chapter Test, 592 Standardized Test Prep: Cumulative Review, 593 xvii T17
11 Surface Area and Volume Check Your Readiness 596 Check Skills You ll Need 598, 608, 617, 624, 631, 638, 646 Quick Check 598, 599, 600, 609, 611, 618, 619, 620, 625, 626, 627, 632, 633, 634, 639, 640, 646, 647, 648 Checkpoint Quiz 623, 644 New 598, 608, 617, 624, 638, 646 Tip 598, 617, 647 Review 653 Video Tutor Help 626 Active Math 625, 633 Homework Help 602, 612, 622, 628, 635, 642, 650 Lesson Quizzes 603, 613, 621, 629, 635, 643, 651 Quiz 653 Chapter Test 656 Geometry at Work 637 Check Your Readiness........................... 596 11-1 Space Figures and Cross Sections....................... 598 Extension: Perspective Drawing, 605 11-2 Surface Areas of Prisms and Cylinders................... 608 Algebra 1 Review: Literal Equations, 607 Guided Problem Solving Understanding Word Problems, 615 Activity Lab Technology: Exploring Surface Area, 616 11-3 Surface Areas of Pyramids and Cones.................... 617 Checkpoint Quiz 1............................... 623 11-4 Volumes of Prisms and Cylinders........................ 624 11-5 Volumes of Pyramids and Cones........................ 631 11-6 Surface Areas and Volumes of Spheres................... 638 Checkpoint Quiz 2............................... 644 11-7 Areas and Volumes of Similar Solids..................... 646 Activity Lab Technology: Exploring Similar Solids, 645 Activity Lab Applying Volume, 658 Test-Taking Strategies: Choosing Cannot Be Determined, 652 Chapter Review, 653 Chapter Test, 656 Standardized Test Prep: Reading Comprehension, 657 T18 xviii
12 Check Your Readiness 660 Check Skills You ll Need 662, 670, 678, 687, 695, 701 Quick Check 663, 664, 665, 670, 671, 673, 679, 680, 681, 688, 689, 690, 695, 696, 697, 701, 702 Checkpoint Quiz 685, 700 New 662, 670, 678, 687, 695, 701 Tip 662, 665, 679, 682, 687, 689, 702 Review 707 Active Math 670, 680, 695 Homework Help 666, 675, 683, 692, 698, 704 Lesson Quizzes 667, 675, 685, 691, 699, 705 Quiz 707 Chapter Test 710 End-of-Course Test 711 Geometry at Work 693 Circles Check Your Readiness........................... 660 12-1 Tangent Lines....................................... 662 12-2 Chords and Arcs..................................... 670 Activity Lab Hands-On: Paper Folding With Circles, 669 Guided Problem Solving Understanding Math Problems, 677 12-3 Inscribed Angles..................................... 678 Checkpoint Quiz 1............................... 685 12-4 Angle Measures and Segment Lengths................... 687 Activity Lab Technology: Exploring Chords and Secants, 686 Extension: Tangent Lines, Tangent Ratios, 694 12-5 Circles in the Coordinate Plane......................... 695 Checkpoint Quiz 2............................... 700 12-6 Locus: A Set of Points................................. 701 Activity Lab Data Analysis: Market Research, 714 Test-Taking Strategies: Using Estimation, 706 Chapter Review, 707 Chapter Test, 710 Standardized Test Prep: Cumulative Review, 711 xix T19