Note: Each chapter concludes with a Summary and Review Exercises | |

Line and Angle Relationships | |

Statements and Reasoning | |

Informal Geometry and Measurement | |

Early Definitions and Postulates | |

Angles and Their Relationships | |

Introduction to Geometric Proof | |

Relationships: Perpendicular Lines | |

The Formal Proof of a Theorem A Look Beyond: Historical Sketch of Euclid | |

Parallel Lines | |

The Parallel Postulate and Special Angles | |

Indirect Proof | |

Proving Lines Parallel | |

The Angles of a Triangle | |

Convex Polygons A Look Beyond: Non-Euclidean Geometries | |

Triangles | |

Congruent Triangles | |

Corresponding Parts of Congruent Triangles | |

Isosceles Triangles | |

Basic Constructions Justified | |

Inequalities in a Triangle A Look Beyond: Historical Sketch of Archimedes | |

Quadrilaterals | |

Properties of a Parallelogram | |

The Parallelogram and Kite | |

The Rectangle, Square, and Rhombus | |

The Trapezoid A Look Beyond: Historical Sketch of Thales | |

Similar Triangles | |

Ratios, Rates, and Proportions | |

Similar Triangles and Polygons | |

The Pythagorean Theorem | |

Special Right Triangles | |

Segments Divided Proportionally A Look Beyond: An Unusual Application of Similar Triangles | |

Circles | |

Circles and Related Segments and Angles | |

More Angle Measures in The Circle | |

Line and Segment Relationships in the Circle | |

Constructions and Inequalities for the Circle | |

Locus of Points | |

Concurrency of Lines A Look Beyond: History of Pi | |

Areas of Polygons and Circles | |

Area and Initial Postulates | |

Perimeter and Area of Polygons | |

Regular Polygons and Area | |

Circumference and Area of a Circle | |

More Area Relationships in the Circle A Look Beyond: Another Look at the Pythagorean Theorem | |

Surfaces and Solids | |

Prisms, Area, and Volume | |

Pyramids, Area, and Volume | |

Cylinders and Cones | |

Polyhedrons and Spheres A Look Beyond: Historical Sketch of Reneacute; Descartes | |

Analytic Geometry | |

The Rectangular Coordinate System | |

Graphs of Linear Equations and Slope | |

Preparing to Do Analytic Proofs | |

Analytic Proofs | |

Equations of Lines A Look Beyond: The Banach-Tarski Paradox | |

Introduction to Trigonometry | |

The Sine Ratio and Applications | |

The Cosine Ratio and Applications | |

The Tangent Ratio and Other Ratios | |

More Trigonometric Relationships A Look Beyond: Radian Measure of Angles | |

Appendix A | |

Appendix B | |

Appendix C | |

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