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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 | |