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Preface | |

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Building a Geometry Vocabulary | |

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The Building Blocks of Geometry | |

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Definitions and Postulates | |

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Inductive Versus Deductive Reasoning | |

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The If ... Then ... Sentence Structure | |

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Review Exercises for Chapter 1 | |

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Measure and Congruence | |

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Measuring Segments and Angles | |

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Betweenness of Points and Rays | |

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Congruence | |

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Midpoint and Bisector | |

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Diagrams and Drawing Conclusions | |

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Properties of Equality and Congruence | |

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Additional Properties of Equality | |

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Review Exercises for Chapter 2 | |

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Angle Pairs and Perpendicular Lines | |

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Supplementary and Complementary Angle Pairs | |

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Adjacent and Vertical Angle Pairs | |

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Theorems Relating to Complementary, Supplementary, and Vertical Angles | |

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Definitions and Theorems Relating to Right Angles and Perpendiculars | |

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Other Types of Proofs in Mathematics | |

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Review Exercises for Chapter 3 | |

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Parallel Lines | |

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Planes and Lines | |

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Properties of Parallel Lines | |

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Converses and Methods of Proving Lines Parallel | |

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The Parallel Postulate | |

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Review Exercises for Chapter 4 | |

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Angles of a Polygon | |

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The Anatomy of a Polygon | |

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Angles of a Triangle | |

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Exterior Angles of a Triangle | |

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Angles of a Polygon | |

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Review Exercises for Chapter 5 | |

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Proving Triangles Are Congruent | |

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Correspondences and Congruent Triangles | |

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Proving Triangles Congruent: SSS, SAS, and ASA Postulates | |

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Proving Overlapping Triangles Congruent | |

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Proving Triangles Congruent: AAS and Hy-Leg Methods | |

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Review Exercises for Chapter 6 | |

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Applying Congruent Triangles | |

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Using Congruent Triangles to Prove Segments and Angles Congruent | |

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Using Congruent Triangles to Prove Special Properties of Lines | |

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Classifying Triangles and Special Segments | |

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The Isosceles Triangle | |

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Double Congruence Proofs | |

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Review Exercises for Chapter 7 | |

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Cumulative Review Exercises: Chapters 1-7 | |

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Geometric Inequalities | |

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Some Basic Properties of Inequalities | |

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Inequality Relationships in a Triangle | |

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The Indirect Method of Proof | |

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Review Exercises for Chapter 8 | |

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Special Quadrilaterals | |

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Classifying Quadrilaterals | |

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Properties of a Parallelogram | |

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Properties of Special Parallelograms | |

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Proving a Quadrilateral Is a Parallelogram | |

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Applications of Parallelograms | |

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Properties of a Trapezoid | |

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Review Exercises for Chapter 9 | |

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Ratio, Proportion, and Similarity | |

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Ratio and Proportion | |

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Proportions in a Triangle | |

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Defining Similar Polygons | |

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Proving Triangles Similar | |

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Proving Lengths of Sides of Similar Triangles in Proportion | |

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Proving Products of Segment Lengths Equal | |

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Review Exercises for Chapter 10 | |

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The Right Triangle | |

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Proportions in a Right Triangle | |

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The Pythagorean Theorem | |

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Special Right-Triangle Relationships | |

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Trigonometric Ratios | |

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Indirect Measurement in a Right Triangle | |

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Review Exercises for Chapter 11 | |

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Cumulative Review Exercises: Chapters 8-11 | |

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Circles and Angle Measurement | |

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The Parts of a Circle | |

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Arcs and Central Angles | |

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Diameters and Chords | |

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Tangents and Secants | |

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Angle Measurement: Vertex on the Circle | |

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Angle Measurement: Vertex in the Interior of the Circle | |

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Angle Measurement: Vertex in the Exterior of the Circle | |

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Using Angle-Measurement Theorems | |

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Review Exercises for Chapter 12 | |

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Chord, Tangent, and Secant Segments | |

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Equidistant Chords | |

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Tangents and Circles | |

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Similar Triangles and Circles | |

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Tangent- and Secant-Segment Relationships | |

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Circumference and Arc Length | |

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Review Exercises for Chapter 13 | |

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Area and Volume | |

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Areas of a Rectangle, Square, and Parallelogram | |

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Areas of a Triangle and Trapezoid | |

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Comparing Areas | |

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Area of a Regular Polygon | |

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Areas of a Circle, Sector, and Segment | |

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Geometric Solids | |

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Review Exercises for Chapter 14 | |

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Coordinate Geometry | |

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The Coordinate Plane | |

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Finding Area Using Coordinates | |

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The Midpoint and Distance Formulas | |

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Slope of a Line | |

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Equation of a Line | |

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Equation of a Circle | |

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Proofs Using Coordinates | |

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Review Exercises for Chapter 15 | |

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Locus and Constructions | |

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Describing Points That Fit One Condition | |

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Describing Points That Fit More Than One Condition | |

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Locus and Coordinates | |

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Basic Constructions | |

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Review Exercises for Chapter 16 | |

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Cumulative Review Exercises: Chapters 12-16 | |

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Some Geometric Formulas Worth Remembering | |

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Glossary | |

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Answers to Chapter Exercises | |

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Solutions to Cumulative Review Exercises | |

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Index | |