Section 1: Lessons 1 10, Investigation 1 Section 1 Overview 2A 1 Points, Lines, and Planes 2 2 Segments 7 3 Angles 13 LAB 1 Construction: Congruent Segments and Angles 19 4 Postulates and Theorems About Points, Lines, and Planes 21 5 More Theorems About Lines and Planes 27 LAB 2 Construction: Perpendicular Line Through a Point on a Line 33 6 Identifying Pairs of Angles 34 LAB 3 Construction: Perpendicular Bisectors and Angle Bisectors 40 7 Using Inductive Reasoning 42 8 Using Formulas in Geometry 47 9 Finding Length: Distance Formula 53 10 Using Conditional Statements 58 Cumulative Assessment Cumulative Test 1, Performance Task 1 INV 1 Investigation: Transversals and Angle Relationships 63 DISTRIBUTED STRANDS Geometry Foundations Logic and Reasoning Construction Coordinate Geometry Triangles: Congruence and Similarity Polygons Quadrilaterals Right Triangles and Trigonometry Circles Solids Transformations T17
Section 2: Lessons 11 20, Investigation 2 Section 2 Overview 66A 11 Finding Midpoints 66 12 Proving Lines Parallel 71 LAB 4 Construction: Parallel Line Through a Point 77 13 Introduction to Triangles 78 14 Disproving Conjectures with Counterexamples 84 15 Introduction to Polygons 89 Cumulative Assessment Cumulative Test 2, Performance Task 2 16 Finding Slopes and Equations of Lines 96 17 More Conditional Statements 103 18 Triangle Theorems Exploration: Developing the Triangle Angle Sum Theorem 109 19 Introduction to Quadrilaterals 115 20 Interpreting Truth Tables 121 Cumulative Assessment Cumulative Test 3, Performance Task 3 INV 2 Investigation: Proving the Pythagorean Theorem 127 T18 Saxon Geometry
Section 3: Lessons 21 30, Investigation 3 Section 3 Overview 130A 21 Laws of Detachment and Syllogism 130 22 Finding Areas of Quadrilaterals 137 23 Introduction to Circles 145 24 Algebraic Proofs 151 25 Triangle Congruence: SSS Exploration: Exploring the SSS Postulate 157 Cumulative Assessment Cumulative Test 4, Performance Task 4 26 Central Angles and Arc Measure 163 27 Two-Column Proofs 169 28 Triangle Congruence: SAS 175 LAB 5 Construction: Congruent Triangles 180 29 Using the Pythagorean Theorem 181 30 Triangle Congruence: ASA and AAS 188 Cumulative Assessment Cumulative Test 5, Performance Task 5 INV 3 Investigation: Exploring Angles of Polygons 194 DISTRIBUTED STRANDS Geometry Foundations Logic and Reasoning Construction Coordinate Geometry Triangles: Congruence and Similarity Quadrilaterals Right Triangles and Trigonometry Circles Solids Transformations Polygons T19
Section 4: Lessons 31 40, Investigation 4 Section 4 Overview 198A 31 Flowchart and Paragraph Proofs 198 32 Altitudes and Medians of Triangles 205 33 Converse of the Pythagorean Theorem 211 34 Properties of Parallelograms Exploration: Exploring Diagonals of Parallelograms 218 35 Finding Arc Lengths and Areas of Sectors 224 Cumulative Assessment Cumulative Test 6, Performance Task 6 36 Right Triangle Congruence Theorems 230 37 Writing Equations of Parallel and Perpendicular Lines 237 38 Perpendicular and Angle Bisectors of Triangles 244 LAB 6 Construction: Circle Through Three Noncollinear Points 250 39 Inequalities in a Triangle 251 40 Finding Perimeters and Areas of Composite Figures 257 Cumulative Assessment Cumulative Test 7, Performance Task 7 INV 4 Investigation: Inequalities in Two Triangles 263 T20 Saxon Geometry
Section 5: Lessons 41 50, Investigation 5 Section 5 Overview 266A 41 Ratios, Proportions, and Similarity 266 42 Finding Distance from a Point to a Line 273 LAB 7 Construction: Perpendicular Through a Point Not on a Line 280 43 Chords, Secants, and Tangents 281 44 Applying Similarity 288 45 Introduction to Coordinate Proofs 295 Cumulative Assessment Cumulative Test 8, Performance Task 8 46 Triangle Similarity: AA, SSS, SAS Exploration: Understanding AA Similarity 301 47 Circles and Inscribed Angles 308 48 Indirect Proofs 315 49 Introduction to Solids 320 50 Geometric Mean 327 Cumulative Assessment Cumulative Test 9, Performance Task 9 INV 5 Investigation: Nets 334 DISTRIBUTED STRANDS Geometry Foundations Logic and Reasoning Construction Coordinate Geometry Triangles: Congruence and Similarity Quadrilaterals Right Triangles and Trigonometry Circles Solids Transformations Polygons T21
Section 6: Lessons 51 60, Investigation 6 Section 6 Overview 336A 51 Properties of Isosceles and Equilateral Triangles 336 52 Properties of Rectangles, Rhombuses, and Squares Exploration: Using Construction Techniques to Draw a Rhombus 343 53 45-45 -90 Right Triangles 349 54 Representing Solids 355 55 Triangle Midsegment Theorem 361 Cumulative Assessment Cumulative Test 10, Performance Task 10 56 30-60 -90 Right Triangles 368 57 Finding Perimeter and Area with Coordinates 374 58 Tangents and Circles, Part 1 381 LAB 8 Construction: Tangent to a Circle 387 59 Finding Surface Areas and Volumes of Prisms 389 60 Proportionality Theorems 396 Cumulative Assessment Cumulative Test 11, Performance Task 11 INV 6 Investigation: Geometric Probability 403 T22 Saxon Geometry
Section 7: Lessons 61 70, Investigation 7 Section 7 Overview 406A 61 Determining If a Quadrilateral is a Parallelogram 406 62 Finding Surface Areas and Volumes of Cylinders Exploration: Analyzing the Net of a Cylinder 412 63 Introduction to Vectors 418 64 Angles Interior to Circles 424 65 Distinguishing Types of Parallelograms 430 Cumulative Assessment Cumulative Test 12, Performance Task 12 66 Finding Perimeters and Areas of Regular Polygons 436 LAB 9 Construction: Regular Polygons 443 67 Introduction to Transformations 445 68 Introduction to Trigonometric Ratios 451 69 Properties of Trapezoids and Kites 457 70 Finding Surface Areas and Volumes of Pyramids 464 Cumulative Assessment Cumulative Test 13, Performance Task 13 INV 7 Investigation: Trigonometric Ratios 470 DISTRIBUTED STRANDS Geometry Foundations Logic and Reasoning Construction Coordinate Geometry Triangles: Congruence and Similarity Quadrilaterals Right Triangles and Trigonometry Circles Solids Transformations Polygons T23
Section 8: Lessons 71 80, Investigation 8 Section 8 Overview 472A 71 Translations 472 72 Tangents and Circles, Part 2 477 73 Applying Trigonometry: Angles of Elevation and Depression Exploration: Making and Using a Hypsometer 483 74 Reflections 490 75 Writing the Equation of a Circle 495 Cumulative Assessment Cumulative Test 14, Performance Task 14 76 Symmetry 500 77 Finding Surface Areas and Volumes of Cones 506 78 Rotations 511 LAB 10 Technology: Transformations Using Geometry Software 516 79 Angles Exterior to Circles 518 80 Finding Surface Areas and Volumes of Spheres 524 Cumulative Assessment Cumulative Test 15, Performance Task 15 INV 8 Investigation: Patterns 529 T24 Saxon Geometry
Section 9: Lessons 81 90, Investigation 9 Section 9 Overview 532A 81 Graphing and Solving Linear Systems 532 82 More Applications of Trigonometry 538 83 Vector Addition 543 84 Dilations 548 85 Cross Sections of Solids 553 Cumulative Assessment Cumulative Test 16, Performance Task 16 86 Determining Chord Length 560 LAB 11 Technology: Intersecting Chords Using Geometry Software 565 87 Area Ratios of Similar Figures 567 88 Graphing and Solving Linear Inequalities 574 89 Vector Decomposition 579 90 Composite Transformations Exploration: Performing Composite Transformations 585 Cumulative Assessment Cumulative Test 17, Performance Task 17 INV 9 Investigation: Tessellations 592 DISTRIBUTED STRANDS Geometry Foundations Logic and Reasoning Construction Coordinate Geometry Triangles: Congruence and Similarity Quadrilaterals Right Triangles and Trigonometry Circles Solids Transformations Polygons T25
Section 10: Lessons 91 100, Investigation 10 Section 10 Overview 594A 91 Introduction to Trigonometric Identities 594 92 Quadrilaterals on the Coordinate Plane 600 LAB 12 Technology: Distinguishing Types of Quadrilaterals Using Geometry Software 606 93 Representing Solids: Orthographic Views Exploration: Drawing Orthographic Views of Objects 607 94 Law of Sines 613 95 Equations of Circles: Translating and Dilating 618 Cumulative Assessment Cumulative Test 18, Performance Task 18 96 Effects of Changing Dimensions on Perimeter and Area 624 97 Concentric Circles 630 98 Law of Cosines 636 99 Volume Ratios of Similar Solids 642 100 Transformation Matrices 648 Cumulative Assessment Cumulative Test 19, Performance Task 19 INV 10 Investigation: Fractals 653 T26 Saxon Geometry
Section 11: Lessons 101 110, Investigation 11 Section 11 Overview 656A 101 Determining Lengths of Segments Intersecting Circles 656 LAB 13 Technology: Exploring Secant Segments Using Geometry Software 662 102 Dilations in the Coordinate Plane 663 103 Frustums of Cones and Pyramids 668 104 Relating Arc Lengths and Chords 674 105 Rotations and Reflections in the Coordinate Plane 680 Cumulative Assessment Cumulative Test 20, Performance Task 20 106 Circumscribed and Inscribed Figures 686 107 Maximizing Area 691 LAB 14 Technology: Maximizing Area Using Geometry Software 696 108 Introduction to Coordinate Space 698 109 Non-Euclidean Geometry Exploration: Exploring Triangle Angles in Spherical Geometry 704 110 Scale Drawings and Maps 709 Cumulative Assessment Cumulative Test 21, Performance Task 21 INV 11 Investigation: Golden Ratio 714 DISTRIBUTED STRANDS Geometry Foundations Logic and Reasoning Construction Coordinate Geometry Triangles: Congruence and Similarity Quadrilaterals Right Triangles and Trigonometry Circles Solids Transformations Polygons T27
Section 12: Lessons 111 120, Investigation 12 Section 12 Overview 716A 111 Finding Distance and Midpoint in Three Dimensions 716 112 Finding Areas of Circle Segments 721 113 Symmetry of Solids and Polyhedra 726 114 Solving and Graphing Systems of Inequalities 731 115 Finding Surface Areas and Volumes of Composite Solids 736 Cumulative Assessment Cumulative Test 22, Performance Task 22 116 Secant, Cosecant, and Cotangent 742 117 Determining Line of Best Fit 747 LAB 15 Technology: Determining Line of Best Fit Using a Graphing Calculator 754 118 Finding Areas of Polygons Using Matrices 756 119 Platonic Solids 761 120 Topology Exploration: Observing Properties of Mobius Strips 767 Cumulative Assessment Cumulative Test 23, Performance Task 23 INV 12 Investigation: Polar Coordinates 773 T28 Saxon Geometry
Skills Bank T776 Properties and Formulas T800 1 Order of Operations and Absolute Value 776 2 Properties of Arithmetic 777 3 Classifying Real Numbers 778 4 Ratios, Proportions, and Percents 779 5 Estimation 780 6 Exponents and Roots 781 7 Scientific Notation and Significant Figures 782 8 Units of Measure 783 9 Converting Units and Rates 784 10 Calculating Percent Error 785 11 Measures of Central Tendency 785 12 Probability 786 13 The Coordinate Plane 788 14 Evaluating Expressions 789 15 Solving Linear Equations and Inequalities 790 16 Transforming Formulas 791 17 Functions 792 18 Binomial Products and Factoring 793 19 Lines in Point-Slope and Standard Forms 794 20 Quadratic Equations and Functions 795 21 Displaying Data 796 22 Problem-Solving Process and Strategies 798 Properties 800 Formulas 802 Symbols 804 Metric Measures 804 Customary Measures 805 Postulates and Theorems T806 Postulates 806 Theorems 807 Glossary Additional Answers Index T813 T828 T895 T29