Preliminary Contents | |

Line and Angle Relations | |

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 | |

Parallel Lines | |

The parallel postulate and special angles | |

Indirect proof | |

Proving lines parallel | |

The angles of a triangle | |

Convex polygons | |

Symmetry and transformations | |

Triangles | |

Congruent triangles | |

Corresponding parts of congruent triangles | |

Isosceles triangles | |

Basic constructions justified | |

Inequalities in a triangle | |

Quadrilaterals | |

Properties of a parallelogram | |

The parallelogram and kite | |

The rectangle, square, and rhombus | |

The trapezoid | |

Similar Triangles | |

Ratios, Rates, and Proportions | |

Similar Polygons | |

Proving Triangles Similar | |

The Pythagorean Theorem | |

Special Right Triangles | |

Segments Divided Proportionately | |

Circles | |

Circles and Related Segments and Angles | |

More Angle Relationships in the Circle | |

Line and Segment Relationships in the Circle | |

Some Constructions and Inequalities for the Circle | |

Locus of Points | |

Concurrence of Lines | |

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 | |

Surfaces and Solids | |

Prisms, area, and volume | |

Pyramids, area, and volume | |

Cylinders and cones | |

Polyhedrons and spheres | |

Analytic Geometry | |

The Rectangular Coordinate System | |

Graphs of Linear Equations and Slope | |

Preparing to do Analytic Proofs | |

Analytic Proofs | |

Equations of Lines | |

Introduction to Trigonometry | |

The Sine Ratio and Applications | |

The Cosine Ratio and Applications | |

The Tangent Ratio and Other Ratios | |

Applications to Acute Triangles | |

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