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

 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