Line and Angle Relationships | |

Sets, 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 | |

Perspective on History: The Development of Geometry | |

Perspective on Application: Patterns | |

Parallel Lines | |

The Parallel Postulate and Special Angles | |

Indirect Proof | |

Proving Lines Parallel | |

The Angles of a Triangle | |

Convex Polygons | |

Symmetry and Transformations | |

Perspective on History: Sketch of Euclid | |

Perspective on Application: Non-Euclidean Geometries | |

Triangles | |

Congruent Triangles | |

Corresponding Parts of Congruent Triangles | |

Isosceles Triangles | |

Basic Constructions Justified | |

Inequalities in a Triangle | |

Perspective on History: Sketch of Archimedes | |

Perspective on Application: Pascal's Triangle | |

Quadrilaterals | |

Properties of a Parallelogram | |

The Parallelogram and Kite | |

The Rectangle, Square, and Rhombus | |

The Trapezoid | |

Perspective on History: Sketch of Thales | |

Perspective on Application: Square Numbers as Sums | |

Similar Triangles | |

Ratios, Rates, and Proportions | |

Similar Polygons | |

Proving Triangles Similar | |

The Pythagorean Theorem | |

Special Right Triangles | |

Segments Divided Proportionally | |

Perspective on History: Ceva's Theorem | |

Perspective on Application: 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 | |

Some Constructions and Inequalities for the Circle | |

Perspective on History: Circumference of the Earth | |

Perspective on Application: Sum of the Interior Angles of a Polygon | |

Locus and Concurrence | |

Locus of Points | |

Concurrence of Lines | |

More About Regular Polygons | |

Perspective on History: The Value of Perspective on Application: The Nine-Point Circle | |

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 | |

Perspective on History: Sketch of Pythagoras | |

Perspective on Application: Another Look at the Pythagorean Theorem | |

Surfaces and Solids | |

Prisms, Area, and Volume | |

Pyramids, Area, and Volume | |

Cylinders and Cones | |

Polyhedrons and Spheres | |

Perspective on History: Sketch of Rene Descartes | |

Perspective on Application: Birds in Flight | |

Analytic Geometry | |

The Rectangular Coordinate System | |

Graphs of Linear Equations and Slope | |

Preparing to do Analytic Proofs | |

Analytic Proofs | |

Equations of Lines | |

Perspective on History: The Banach-Tarski Paradox | |

Perspective on Application: The Point-of-Division Formulas | |

Introduction to Trigonometry | |

The Sine Ratio and Applications | |

The Cosine Ratio and Applications | |

The Tangent Ratio and Other Ratios | |

Applications with Acute Triangles. | |

Perspective on History: Sketch of Plato | |

Perspective on Application: Radian Measure of Angles | |

Appendices | |

Algebra review | |

Summary of Constructions, Postulates, and Theorems and Corollaries | |

Table of Contents provided by Publisher. All Rights Reserved. |