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