1. Points and Lines
    1. Dots as Points
    2. Locations as Points
    3. Ordered Pairs as Points
    4. Points in Networks
    5. Drawing in Perspective
    6. The Need for Undefined Terms
    7. Postulates for Euclidean Geometry
    8. Betweenness and Distance
  2. The Language and Logic of Geometry
    1. The Need for Definitions
    2. "If-Then" Statements
    3. Converses
    4. Good Definitions
    5. Unions and Intersections of Figures
    6. Polygons
    7. Using an Automatic Drawer: The Triangle Inequality
    8. Conjectures
  3. Angles and Lines
    1. Angles and Their Measures
    2. Arcs and Rotations
    3. Properties of Angles
    4. Algebra Properties Used in Geometry
    5. One-Step Proof Arguments
    6. Parallel Lines
    7. Perpendicular Lines
    8. Drawing Parallel and Perpendicular Lines
  4. From Reflections to Congruence
    1. Reflecting Points
    2. Reflecting Figures
    3. Miniature Golf and Billiards
    4. Composing Reflections over Parallel Lines
    5. Composing Reflections over Intersecting Lines
    6. Translations and Vectors
    7. Isometries
    8. When are Figures Congruent
  5. Proofs Using Congruence
    1. Corresponding Parts of Congruent Figures
    2. Congruence and Equality
    3. One-Step Congruence Proofs
    4. Proofs Using Transitivity
    5. Proofs Using Reflections
    6. Auxiliary Figures and Uniqueness
    7. Sums of Angle Measures in Polygons
  6. Polygons and Symmetry
    1. Reflection-Symmetric Figures
    2. Isosceles Triangles
    3. Types of Quadrilaterals
    4. Properties of Kites
    5. Properties of Trapezoids
    6. Rotation Symmetry
    7. Regular Polygons
    8. Regular Polygons and Schedules
  7. Triangle Congruence
    1. Drawing Triangles
    2. Triangle Congruence Theorems
    3. Proofs Using Triangle Congruence Theorems
    4. Overlapping Triangles
    5. The SSA Condition and HL Congruence
    6. Tessellations
    7. Properties of Parallelograms
    8. Sufficient Conditions for Parallelograms
    9. Exterior Angles
  8. Perimeters and Areas
    1. Perimeter Formulas
    2. Fundamental Properties of Area
    3. Areas of Irregular Regions
    4. Areas of Triangles
    5. Areas of Trapezoids
    6. The Pythagorean Theorem
    7. Arc Length and Circumference
    8. The Area of a Circle
  9. Three-Dimensional Figures
    1. Points, Lines, and Planes in Space
    2. Parallel and Perpendicular Lines and Planes
    3. Prisms and Cylinders
    4. Pyramids and Cones
    5. Spheres and Sections
    6. Reflection Symmetry in Space
    7. Viewing Solids and Surfaces
    8. Making Surfaces
    9. Maps and the Four-Color Theorem
  10. Surface Areas and Volumes
    1. Surface Areas of Prisms and Cylinders
    2. Surface Areas of Pyramids and Cones
    3. Fundamental Properties of Volume
    4. Multiplication, Area, and Volume
    5. Volumes of Prisms and Cylinders
    6. Organizing Formulas
    7. Volumes of Pyramids and Cones
    8. The Volume of a Sphere
    9. The Surface Area of a Sphere
  11. Indirect and Coordinate Proofs
    1. The Logic of Making Conclusions
    2. Negations
    3. Ruling Out Possibilities
    4. Indirect Proof
    5. Proofs with Coordinates
    6. The Distance Formula
    7. Equations for Circles
    8. Means and Midpoints
    9. Three-Dimensional Coordinates
  12. Similarity
    1. The Transformation Sk
    2. Size Changes
    3. Properties of Size Changes
    4. Properties of Size Changes
    5. Similar Figures
    6. The Fundamental Theorem of Similarity
    7. Can There Be Giants?
  13. Similar Triangles and Trigonometry
    1. The SSS Similarity Theorem
    2. The AA and SAS Similarity Theorem
    3. The Side-Splitting Theorem
    4. Geometric means in Right Triangles
    5. Special Right Triangles
    6. The Tangent of an Angle
    7. The Sine and Cosine Ratios
    8. More Work with Vectors and Area
  14. Further Work with Circles
    1. Chord Length and Arc Measure
    2. The Inscribed Angle Theorem
    3. Locating the Center of a Circle
    4. Angles Formed by Chords or Secants
    5. Tangents to Circles and Spheres
    6. Angles Formed by Tangents
    7. Lengths of Chords, Secants, and Tangents
    8. The Isoperimetric Inequality
    9. The Isoperimetric Inequality in Three Dimensions
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