Efnisyfirlit

• Title Page
• Copyright Page
• Contents
• Preface
• Acknowledgments
• Foreword
• Index of Applications
• Chapter P: Preliminary Concepts
  • P.1 Sets and Geometry
  • P.2 Statements and Reasoning
  • P.3 Informal Geometry and Measurement
  • PERSPECTIVE ON HISTORY: Our Greek Heritage
  • PERSPECTIVE ON APPLICATIONS: One-to-One Correspondence
  • Summary
  • Review Exercises
  • Chapter P Test
• Chapter 1: Line and Angle Relationships
  • 1.1 Early Definitions and Postulates
  • 1.2 Angles and Their Relationships
  • 1.3 Introduction to Geometric Proof
  • 1.4 Relationships: Perpendicular Lines
  • 1.5 The Formal Proof of a Theorem
  • PERSPECTIVE ON HISTORY: The Development of Geometry
  • PERSPECTIVE ON APPLICATIONS: Patterns
  • Summary
  • Review Exercises
  • Chapter 1 Test
• Chapter 2: Parallel Lines
  • 2.1 The Parallel Postulate and Special Angles
  • 2.2 Indirect Proof
  • 2.3 Proving Lines Parallel
  • 2.4 The Angles of a Triangle
  • 2.5 Convex Polygons
  • 2.6 Symmetry and Transformations
  • PERSPECTIVE ON HISTORY: Sketch of Euclid
  • PERSPECTIVE ON APPLICATIONS: Non-Euclidean Geometries
  • Summary
  • Review Exercises
  • Chapter 2 Test
• Chapter 3: Triangles
  • 3.1 Congruent Triangles
  • 3.2 Corresponding Parts of Congruent Triangles
  • 3.3 Isosceles Triangles
  • 3.4 Basic Constructions Justified
  • 3.5 Inequalities in a Triangle
  • PERSPECTIVE ON HISTORY: Sketch of Archimedes
  • PERSPECTIVE ON APPLICATIONS: The Geodesic Dome
  • Summary
  • Review Exercises
  • Chapter 3 Test
• Chapter 4: Quadrilaterals
  • 4.1 Properties of a Parallelogram
  • 4.2 The Parallelogram and Kite
  • 4.3 The Rectangle, Square, and Rhombus
  • 4.4 The Trapezoid
  • PERSPECTIVE ON HISTORY: Sketch of Thales
  • PERSPECTIVE ON APPLICATIONS: Square Number as Sums
  • Summary
  • Review Exercises
  • Chapter 4 Test
• Chapter 5: Similar Triangles
  • 5.1 Ratios, Rates, and Proportions
  • 5.2 Similar Polygons
  • 5.3 Proving Triangles Similar
  • 5.4 The Pythagorean Theorem
  • 5.5 Special Right Triangles
  • 5.6 Segments Divided Proportionally
  • PERSPECTIVE ON HISTORY: Ceva•fs Proof
  • PERSPECTIVE ON APPLICATIONS: Generating Pythagorean Triples
  • Summary
  • Review Exercises
  • Chapter 5 Test
• Chapter 6: Circles
  • 6.1 Circles and Related Segments and Angles
  • 6.2 More Angle Measures in the Circle
  • 6.3 L ine and Segment Relationships in the Circle
  • 6.4 Some Constructions and Inequalities for the Circle
  • PERSPECTIVE ON HISTORY: Circumference of the Earth
  • PERSPECTIVE ON APPLICATIONS: Sum of Interior Angles of a Polygon
  • Summary
  • Review Exercises
  • Chapter 6 Test
• Chapter 7: Locus and Concurrence
  • 7.1 Locus of Points
  • 7.2 Concurrence of Lines
  • 7.3 More About Regular Polygons
  • PERSPECTIVE ON HISTORY: The Value of p
  • PERSPECTIVE ON APPLICATIONS: The Nine-Point Circle
  • Summary
  • Review Exercises
  • Chapter 7 Test
• Chapter 8: Areas of Polygons and Circles
  • 8.1 Area and Initial Postulates
  • 8.2 Perimeter and Area of Polygons
  • 8.3 Regular Polygons and Area
  • 8.4 Circumference and Area of a Circle
  • 8.5 More Area Relationships in the Circle
  • PERSPECTIVE ON HISTORY: Sketch of Pythagoras
  • PERSPECTIVE ON APPLICATIONS: Another Look at the Pythagorean Theorem
  • Summary
  • Review Exercises
  • Chapter 8 Test
• Chapter 9: Surfaces and Solids
  • 9.1 Prisms, Area, and Volume
  • 9.2 Pyramids, Area, and Volume
  • 9.3 Cylinders and Cones
  • 9.4 Polyhedrons and Spheres
  • PERSPECTIVE ON HISTORY: Sketch of Rene Descartes
  • PERSPECTIVE ON APPLICATIONS: Birds in Flight
  • Summary
  • Review Exercises
  • Chapter 9 Test
• Chapter 10: Analytic Geometry
  • 10.1 The Rectangular Coordinate System
  • 10.2 Graphs of Linear Equations and Slope
  • 10.3 Preparing to Do Analytic Proofs
  • 10.4 Analytic Proofs
  • 10.5 Equations of Lines
  • 10.6 The Three-Dimensional Coordinate System
  • PERSPECTIVE ON HISTORY: The Banach-Tarski Paradox
  • PERSPECTIVE ON APPLICATIONS: The Point-of-Division Formulas
  • Summary
  • Review Exercises
  • Chapter 10 Test
• Chapter 11: Introduction to Trigonometry
  • 11.1 The Sine Ratio and Applications
  • 11.2 The Cosine Ratio and Applications
  • 11.3 The Tangent Ratio and Other Ratios
  • 11.4 Applications with Acute Triangles
  • PERSPECTIVE ON HISTORY: Sketch of Plato
  • PERSPECTIVE ON APPLICATIONS: Radian Measure of Angles
  • Summary
  • Review Exercises
  • Chapter 11 Test
• APPENDIX A: Algebra Review
• APPENDIX B: Summary of Constructions, Postulates, Theorems, Lemmas, and Corollaries
• Selected Exercises and Proofs
• Glossary
• Index

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