Chapter 1

Shapes And Transformations

1.1 Course Introduction Problems 1.1.1 Creating a Quilt Using Symmetry p.5
1.1.2 Making Predictions and Investigating Results p.11
1.1.3 p.15
1.1.4 Logical Arguments p.19
1.1.5 p.24
1.2 Transformations and Symmetry 1.2.1 Spatial Visualization and Reflections p.29
1.2.2 Rigid Transformations: Rotations and Translations p.34
1.2.3 Using Transformations p.39
1.2.4 Using Transformations to Create Shapes p.42
1.2.5 Symmetry p.46
1.3 Shapes and Probability 1.3.1 Attributes and Characteristics of Shapes p.52
1.3.2 More Characteristics of Shapes p.55
1.3.3 Introduction to Probability p.60
Chapter Closure p.64

Chapter 2

Angles And Measurements

2.1 Angle Relationships 2.1.1 Complementary, Supplementary, and Vertical Angles p.74
2.1.2 Angles Formed by Transversals p.78
2.1.3 More Angles Formed by Transversals p.83
2.1.4 Angles in a Triangle p.89
2.1.5 Applying Angle Relationships p.93
2.2 Area 2.2.1 Units of Measure p.100
2.2.2 Areas of Triangles and Composite Shapes p.102
2.2.3 Areas of Parallelograms and Trapezoids p.105
2.2.4 Heights and Area p.112
2.3 The Pythagorean Theorem 2.3.1 Squares and Square Roots p.113
2.3.2 Triangle Inequality p.120
2.3.3 The Pythagorean Theorem p.122
Chapter Closure p.127

Chapter 3

Justification And Similarity

3.1 Introduction to Similarity 3.1.1 Similarity p.138
3.1.2 Proportional Growth and Ratios p.142
3.1.3 Using Ratios of Similarity p.146
3.1.4 Applications and Notation p.150
3.2 Triangle Similarity 3.2.1 Conditions for Triangle Similarity p.155
3.2.2 Creating a Flowchart p.160
3.2.3 Triangle Similarity and Congruence p.164
3.2.4 More Conditions for Triangle Similarity p.167
3.2.5 Determining Similarity p.171
3.2.6 Applying Similarity p.174
Chapter Closure p.177

Chapter 4

Trigonometry And Probability

4.1 The Tangent Ratio 4.1.1 Constant Ratios in Right Angles p.190
4.1.2 Connecting Slope Ratios to Specific Angles p.192
4.1.3 Expanding the Trig Table p.196
4.1.4 The Tangent Ratio p.199
4.1.5 Applying the Tangent Ratio p.203
4.2 Probability Models 4.2.1 Introduction to Probability Models p.207
4.2.2 Theoretical and Experimental Probability p.209
4.2.3 Using an Area Model p.215
4.2.4 Choosing a Probability Model p.220
4.2.5 Optional: Applications of Probability Methods p.223
Chapter Closure p.226

Chapter 5

Trigonometry And Triangle Tool Kit

5.1 Trigonometry 5.1.1 Sine and Cosine Ratios p.235
5.1.2 Selecting a Trig Tool p.239
5.1.3 Inverse Trigonometry p.243
5.1.4 Trigonometric Applications p.246
5.2 Special Right Triangles 5.2.1 Special Right Triangles p.250
5.2.2 Pythagorean Triples p.254
5.3 Completing the Triangle Toolkit 5.3.1 Finding Missing Parts of Triangles p.257
5.3.2 Law of Sines p.262
5.3.3 Law of Cosines p.265
5.3.4 Optional: Ambiguous Triangles p.269
5.3.5 Choosing a Tool p.273
Chapter Closure p.280

Chapter 6

Congruent Triangles

6.1 Congruent Triangles 6.1.1 Congruent Triangles p.291
6.1.2 Conditions for Triangle Congruence p.295
6.1.3 Flowcharts for Congruence p.298
6.1.4 Converses p.304
6.2 Closure Activities 6.2.1 Angles on a Pool Table p.308
6.2.2 Investigating a Triangle p.310
6.2.3 Creating a Mathematical Model p.313
6.2.4 Analyzing a Game p.317
6.2.5 Using Transformations and Symmetry to Create a Snowflake p.322
Chapter Closure p.326

Chapter 7

Proof And Quadrilaterals

7.1 Introduction to Chapters 7 - 12 7.1.1 Properties of a Circle p.338
7.1.2 Building a Tetrahedron p.341
7.1.3 Shortest Distance Problems p.346
7.1.4 Using Symmetry to Study Polygons p.351
7.2 Proof and Quadrilaterals 7.2.1 Special Quadrilaterals and Proof p.355
7.2.2 Properties of Rhombi p.358
7.2.3 More Proof with Congruent Triangles p.361
7.2.4 More Properties of Quadrilaterals p.364
7.2.5 Two-Column Proofs p.367
7.2.6 Explore-Conjecture-Prove p.372
7.3 Coordinate Geometry 7.3.1 Studying Quadrilaterals on a Coordinate Grid p.374
7.3.2 Coordinate Geometry and Midpoints p.379
7.3.3 Quadrilaterals on a Coordinate Plane p.382
Chapter Closure p.386

Chapter 8

Polygons And Circles

8.1 Angles and Area of a Polygon 8.1.1 Pinwheels and Polygons p.396
8.1.2 Interior Angles of a Polygon p.400
8.1.3 Angles of Regular Polygons p.404
8.1.4 Regular Polygon Angle Connections p.407
8.1.5 Finding the Area of Regular Polygons p.410
8.2 Ratio of the Area of Similar Figures 8.2.1 Area Ratios of Similar Figures p.415
8.2.2 Ratios of Similarity p.419
8.3 Area and Circumference of a Circle 8.3.1 A Special Ratio p.422
8.3.2 Area and Circumference of Circles p.426
8.3.3 Circles in Context p.430
Chapter Closure p.436

Chapter 9

Solids And Constructions

9.1 Three-dimensional Solids and Their Measurement 9.1.1 Three-Dimensional Solids p.445
9.1.2 Volume and Surface Area of Prisms p.449
9.1.3 Prisms and Cylinders p.452
9.1.4 Volumes of Similar Solids p.455
9.1.5 Ratios of Similarity p.458
9.2 Constructing Geometric Shapes and Relationships 9.2.1 Introduction to Construction p.461
9.2.2 Constructing Bisectors p.465
9.2.3 More Exploration with Constructions p.469
9.2.4 Finding a Centroid p.472
Chapter Closure p.475

Chapter 10

Circles And Expected Value

10.1 The Relationships Between Angles, Arcs, and Line Segments in a Circle 10.1.1 Introduction to Chords p.486
10.1.2 Angles and Arcs p.490
10.1.3 Chords and Angles p.495
10.1.4 Tangents and Chords p.498
10.1.5 Problem Solving with Circles p.501
10.2 Circles Inscribed in Triangles 10.2.1 Designing Spinners p.505
10.2.2 Expected Value p.509
10.2.3 More Expected Value p.512
10.3 Equation of a Circle 10.3.1 The Equation of a Circle p.516
Chapter Closure p.520

Chapter 11

Solids And Circles

11.1 Pyramids, Cones, Spheres 11.1.1 Platonic Solids p.530
11.1.2 Pyramids p.535
11.1.3 Volume of a Pyramid p.539
11.1.4 Surface Area and Volume of a Cone p.543
11.1.5 Surface Are and Volume of a Sphere p.547
11.2 More Circle Relationships 11.2.1 Coordinates on a Sphere p.552
11.2.2 Tangents and Arcs p.555
11.2.3 Secant and Tangent Relationships p.561
Chapter Closure p.566

Chapter 12

Comics And Closure

12.1 Conic Sections 12.1.1 Introduction to Conic Sections p.575
12.1.2 Graphing Parabolas Using The Focus and Directrix p.578
12.1.3 Circles and Ellipses p.581
12.1.4 The Hyperbola p.585
12.1.5 Conic Equations and Graphs p.589
12.2 Closure Activities 12.2.1 Using Coordinate Geometry and Construction to Explore Shapes p.592
12.2.2 Euler's Formula for Polyhedra p.595
12.2.3 The Golden Ratio p.600
12.2.4 Using Geometry to Find Probability p.603
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