Table of Contents

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**Chapter 1: Problem Solving**

**Chapter 2: Angles and Measurement**

**Chapter 3: Justification and Similarity**

**Chapter 4: Trigonometry and Probability**

**Chapter 5: Completing the Triangle Toolkit**

**Chapter 6: Congruent Triangles**

**Chapter 7: Proof and Quadrilaterals**

**Chapter 8: Polygons and Circles**

**Chapter 9: Solids and Constructions**

**Chapter 10: Circles and Expected Value**

**Chapter 11: Solids and Circles**

**Chapter 12: Conics and Closure**

**Appendices**

**Glossary**

Index

Opening | 1.OP | Chapter Opening |

Section 1.1 | 1.1.1 | Creating a Quilt Using Symmetry |

1.1.2 | Making Predictions and Investigating Results | |

1.1.3 | Perimeter and Area of Enlarging Tile Patterns | |

1.1.4 | Logical Arguments | |

1.1.5 | Building a Kaleidoscope | |

Section 1.2 | 1.2.1 | Spatial Visualization and Reflections |

1.2.2 | Rigid Transformations: Rotations and Translations | |

1.2.3 | Using Transformations | |

1.2.4 | Using Transformations to Create Shapes | |

1.2.5 | Symmetry | |

Section 1.3 | 1.3.1 | Attributes and Characteristics of Shapes |

1.3.2 | More Characteristics of Shapes | |

1.3.3 | Introduction to Probability | |

Closure | 1.CL | Chapter Closure |

Opening | 2.OP | Chapter Opening |

Section 2.1 | 2.1.1 | Complementary, Supplementary, and Vertical Angles |

2.1.2 | Angles Formed by Transversals | |

2.1.3 | More Angles Formed by Transversals | |

2.1.4 | Angles in a Triangle | |

2.1.5 | Applying Angle Relationships | |

Section 2.2 | 2.2.1 | Units of Measure |

2.2.2 | Areas of Triangles and Composite Shapes | |

2.2.3 | Areas of Parallelograms and Trapezoids | |

2.2.4 | Heights and Area | |

Section 2.3 | 2.3.1 | Squares and Square Roots |

2.3.2 | Triangle Inequality | |

2.3.3 | The Pythagorean Theorem | |

Closure | 2.CL | Chapter Closure |

Opening | 3.OP | Chapter Opening |

Section 3.1 | 3.1.1 | Similarity |

3.1.2 | Proportional Growth and Ratios | |

3.1.3 | Using Ratios of Similarity | |

3.1.4 | Applications and Notation | |

Section 3.2 | 3.2.1 | Conditions for Triangle Similarity |

3.2.2 | Creating a Flowchart | |

3.2.3 | Triangle Similarity and Congruence | |

3.2.4 | More Conditions for Triangle Similarity | |

3.2.5 | Determining Similarity | |

3.2.6 | Applying Similarity | |

Closure | 3.CL | Chapter Closure |

Opening | 4.OP | Chapter Opening |

Section 4.1 | 4.1.1 | Constant Ratios in Right Triangles |

4.1.2 | Connecting Slope Ratios to Specific Angles | |

4.1.3 | Expanding the Trig Table | |

4.1.4 | The Tangent Ratio | |

4.1.5 | Applying the Tangent Ratio | |

Section 4.2 | 4.2.1 | Introduction to Probability Models |

4.2.2 | Theoretical and Experimental Probability | |

4.2.3 | Using an Area Model | |

4.2.4 | Choosing a Probability Model | |

4.2.5 | Optional: Applications of Probability Methods | |

Closure | 4.CL | Chapter Closure |

Opening | 5.OP | Chapter Opening |

Section 5.1 | 5.1.1 | Sine and Cosine Ratios |

5.1.2 | Selecting a Trig Tool | |

5.1.3 | Inverse Trigonometry | |

5.1.4 | Trigonometric Applications | |

Section 5.2 | 5.2.1 | Special Right Triangles |

5.2.2 | Pythagorean Triples | |

Section 5.3 | 5.3.1 | Finding Missing Parts of Triangles |

5.3.2 | Law of Sines | |

5.3.3 | Law of Cosines | |

5.3.4 | Ambiguous Triangles | |

5.3.5 | Choosing a Tool | |

Closure | 5.CL | Chapter Closure |

Opening | 6.OP | Chapter Opening |

Section 6.1 | 6.1.1 | Congruent Triangles |

6.1.2 | Conditions for Triangle Congruence | |

6.1.3 | Flowcharts for Congruence | |

6.1.4 | Converses | |

Section 6.2 | 6.2.1 | Angles on a Pool Table |

6.2.2 | Investigating a Triangle | |

6.2.3 | Creating a Mathematical Model | |

6.2.4 | Analyzing a Game | |

6.2.5 | Using Transformations and Symmetry to Create a Snowflake | |

Closure | 6.CL | Chapter Closure |

Opening | 7.OP | Chapter Opening |

Section 7.1 | 7.1.1 | Properties of a Circle |

7.1.2 | Building a Tetrahedron | |

7.1.3 | Shortest Distance Problems | |

7.1.4 | Using Symmetry to Study Polygons | |

Section 7.2 | 7.2.1 | Special Quadrilaterals and Proof |

7.2.2 | Properties of Rhombi | |

7.2.3 | More Proof with Congruent Triangles | |

7.2.4 | More Properties of Quadrilaterals | |

7.2.5 | Two-Column Proofs | |

7.2.6 | Explore-Conjecture-Prove | |

Section 7.3 | 7.3.1 | Studying Quadrilaterals on a Coordinate Grid |

7.3.2 | Coordinate Geometry and Midpoints | |

7.3.3 | Quadrilaterals on a Coordinate Plane | |

Closure | 7.CL | Chapter Closure |

Opening | 8.OP | Chapter Opening |

Section 8.1 | 8.1.1 | Pinwheels and Polygons |

8.1.2 | Interior Angles of a Polygon | |

8.1.3 | Angles of Regular Polygons | |

8.1.4 | Regular Polygon Angle Connections | |

8.1.5 | Finding the Area of Regular Polygons | |

Section 8.2 | 8.2.1 | Area Ratios of Similar Figures |

8.2.2 | Ratios of Similarity | |

Section 8.3 | 8.3.1 | A Special Ratio |

8.3.2 | Area and Circumference of Circles | |

8.3.3 | Circles in Context | |

Closure | 8.CL | Chapter Closure |

Opening | 9.OP | Chapter Opening |

Section 9.1 | 9.1.1 | Three-Dimensional Solids |

9.1.2 | Volume and Surface Area of Prisms | |

9.1.3 | Prisms and Cylinders | |

9.1.4 | Volumes of Similar Solids | |

9.1.5 | Ratios of Similarity | |

Section 9.2 | 9.2.1 | Introduction to Construction |

9.2.2 | Constructing Bisectors | |

9.2.3 | More Exploration with Constructions | |

9.2.4 | Finding a Centroid | |

Closure | 9.CL | Chapter Closure |

Opening | 10.OP | Chapter Opening |

Section 10.1 | 10.1.1 | Introduction to Chords |

10.1.2 | Angles and Arcs | |

10.1.3 | Chords and Angles | |

10.1.4 | Tangents and Chords | |

10.1.5 | Problem Solving with Circles | |

Section 10.2 | 10.2.1 | Designing Spinners |

10.2.2 | Expected Value | |

10.2.3 | More Expected Value | |

Section 10.3 | 10.3.1 | The Equation of a Circle |

Section 10.4 | 10.4 | Laws of Exponents |

Closure | 10.CL | Chapter Closure |

Opening | 11.OP | Chapter Opening |

Section 11.1 | 11.1.1 | Platonic Solids |

11.1.2 | Pyramids | |

11.1.3 | Volume of a Pyramid | |

11.1.4 | Surface Area and Volume of a Cone | |

11.1.5 | Surface Area and Volume of a Sphere | |

Section 11.2 | 11.2.1 | Coordinates on a Sphere |

11.2.2 | Tangents and Arcs | |

11.2.3 | Secant and Tangent Relationships | |

Section 11.3 | 11.3.1 | Relation Treasure Hunt |

Closure | 11.CL | Chapter Closure |

Opening | 12.OP | Chapter Opening |

Section 12.1 | 12.1.1 | Introduction to Conic Sections |

12.1.2 | Graphing Parabolas Using the Focus and Directrix | |

12.1.3 | Circles and Ellipses | |

12.1.4 | The Hyperbola | |

12.1.5 | Conic Equations and Graphs | |

Section 12.2 | 12.2.1 | Using Coordinate Geometry and Construction to Explore Shapes |

12.2.2 | Euler’s Formula for Polyhedra | |

12.2.3 | The Golden Ratio | |

12.2.4 | Using Geometry to Find Probability | |

Closure | 12.CL | Chapter Closure |

A | Points, Lines, and Planes | |

B | Euclidean Geometry | |

C | Non-Euclidean Geometry |

Index