Efnisyfirlit

• Cover Page
• Title Page
• Copyright Page
• Dedication
• Letter from the Authors
• Preface
• Acknowledgements
• Foreword
• P. Preliminary Concepts
  • P.1. Sets and Geometry
    • Sets and Sets of Numbers
    • Sets of Points
    • Intersection and Union of Sets
    • Sets and Venn Diagrams
    • P.1. Exercises
  • P.2. Statements and Reasoning
    • Statements
    • Reasoning
    • Venn Diagrams
    • P.2. Exercises
  • P.3. Informal Geometry and Measurement
    • Measuring Line Segments
    • Measuring Angles
    • Constructions
    • P.3. Exercises
    • Perspective on History: Our Greek Heritage
    • Perspective on Applications: One-to-One Correspondence
  • Summary
  • Overview
  • Review Exercises
  • Chapter P Test
• 1. Line and Angle Relationships
  • 1.1. Early Definitions and Postulates
    • A Mathematical System
    • Characteristics of a Good Definition
    • Initial Postulates
    • 1.1. Exercises
  • 1.2. Angles and Their Relationships
    • Types of Angles
    • Classifying Pairs of Angles
    • Constructions with Angles
    • 1.2. Exercises
  • 1.3. Introduction to Geometric Proof
    • Sample Proofs
    • 1.3. Exercises
  • 1.4. Relationships: Perpendicular Lines
    • Relations
    • Constructions Leading to Perpendicular Lines
    • 1.4. Exercises
  • 1.5. The Formal Proof of a Theorem
    • The Written Parts of a Formal Proof
    • Converse of a Statement
    • 1.5. Exercises
    • Perspective on History: The Development of Geometry
    • Perspective on Applications: Patterns
  • Summary
  • Overview
  • Review Exercises
  • Chapter 1 Test
• 2. Parallel Lines
  • 2.1. The Parallel Postulate and Special Angles
    • Perpendicular Lines
    • Parallel Lines
    • Euclidean Geometry
    • Parallel Lines and Congruent Angles
    • Parallel Lines and Supplementary Angles
    • 2.1. Exercises
  • 2.2. Indirect Proof
    • The Law of Negative Inference (Contraposition)
    • Indirect Proof
    • 2.2. Exercises
  • 2.3. Proving Lines Parallel
    • 2.3. Exercises
  • 2.4. The Angles of a Triangle
    • 2.4. Exercises
  • 2.5. Convex Polygons
    • Diagonals of a Polygon
    • Sum of the Interior Angles of a Polygon
    • Regular Polygons
    • Polygrams
    • 2.5. Exercises
  • 2.6. Symmetry and Transformations
    • Line Symmetry
    • Point Symmetry
    • Transformations
    • 2.6. Exercises
    • Perspective on History: Sketch of Euclid
    • Perspective on Applications: Non-Euclidean Geometries
  • Summary
  • Overview
  • Review Exercises
  • Chapter 2 Test
• 3. Triangles
  • 3.1. Congruent Triangles
    • SSS (Method for Proving Triangles Congruent)
    • SAS (Method for Proving Triangles Congruent)
    • Overlapping Triangles
    • ASA (Method for Proving Triangles Congruent)
    • AAS (Method for Proving Triangles Congruent)
    • 3.1. Exercises
  • 3.2. Corresponding Parts of Congruent Triangles
    • Suggestions for Proving Triangles Congruent
    • Right Triangles
    • HL (Method for Proving Triangles Congruent)
    • The Pythagorean Theorem
    • 3.2. Exercises
  • 3.3. Isosceles Triangles
    • 3.3. Exercises
  • 3.4. Basic Constructions Justified
    • 3.4. Exercises
  • 3.5. Inequalities in a Triangle
    • Lemmas (Helping Theorems)
    • 3.5. Exercises
    • Perspective on History: Sketch of Archimedes
    • Perspective on Applications: The Geodesic Dome
  • Summary
  • Overview
  • Review Exercises
  • Chapter 3 Test
• 4. Quadrilaterals
  • 4.1. Properties of a Parallelogram
    • Speed and Direction of Aircraft
    • 4.1. Exercises
  • 4.2. The Parallelogram and Kite
    • The Parallelogram
    • The Kite
    • 4.2. Exercises
  • 4.3. The Rectangle, Square, and Rhombus
    • The Rectangle
    • The Square
    • The Rhombus
    • The Pythagorean Theorem
    • 4.3. Exercises
  • 4.4. The Trapezoid
    • 4.4. Exercises
    • Perspective on History: Sketch of Thales
    • Perspective on Applications: Square Number as Sums
  • Summary
  • Overview
  • Review Exercises
  • Chapter 4 Test
• 5. Similar Triangles
  • 5.1. Ratios, Rates, and Proportions
    • 5.1. Exercises
  • 5.2. Similar Polygons
    • 5.2. Exercises
  • 5.3. Proving Triangles Similar
    • 5.3. Exercises
  • 5.4. The Pythagorean Theorem
    • Pythagorean Triples
    • The Converse of the Pythagorean Theorem
    • 5.4. Exercises
  • 5.5. Special Right Triangles
    • The 45 ° - 45 ° - 90 ° Right Triangle
    • The 30 ° - 60 ° - 90 ° Right Triangle
    • 5.5. Exercises
  • 5.6. Segments Divided Proportionally
    • Ceva’s Theorem
    • 5.6. Exercises
    • Perspective on History: Proof
    • Perspective on Applications: Generating Pythagorean Triples
  • Summary
  • Overview
  • Review Exercises
  • Chapter 5 Test
• 6. Circles
  • 6.1. Circles and Related Segments and Angles
    • Angle and Arc Relationships in the Circle
    • 6.1. Exercises
  • 6.2. More Angle Measures in the Circle
    • 6.2. Exercises
  • 6.3. Line and Segment Relationships in the Circle
    • Circles That Are Tangent
    • Common Tangent Lines to Circles
    • Lengths of Line Segments in a Circle
    • 6.3. Exercises
  • 6.4. Some Constructions and Inequalities for the Circle
    • Constructions of Tangents to Circles
    • Inequalities in the Circle
    • 6.4. Exercises
    • Perspective on History: Circumference of the Earth
    • Perspective on Applications: Sum of Interior Angles of a Polygon
  • Summary
  • Overview
  • Review Exercises
  • Chapter 6 Test
• 7. Locus and Concurrence
  • 7.1. Locus of Points
    • Parabolas
    • 7.1. Exercises
  • 7.2. Concurrence of Lines
    • 7.2. Exercises
  • 7.3. More About Regular Polygons
    • 7.3. Exercises
    • Perspective on History: The Value of π
    • Perspective on Applications: The Nine-Point Circle
  • Summary
  • Overview
  • Review Exercises
  • Chapter 7 Test
• 8. Areas of Polygons and Circles
  • 8.1. Area and Initial Postulates
    • Area of a Rectangle
    • Area of a Parallelogram
    • Area of a Triangle
    • 8.1. Exercises
  • 8.2. Perimeter and Area of Polygons
    • Heron’s Formula
    • Area of a Trapezoid
    • Quadrilaterals with Perpendicular Diagonals
    • Area of a Rhombus
    • Area of a Kite
    • Areas of Similar Polygons
    • 8.2. Exercises
  • 8.3. Regular Polygons and Area
    • Area of a Regular Polygon
    • 8.3. Exercises
  • 8.4. Circumference and Area of a Circle
    • Value of π
    • Length of an Arc
    • Limits
    • Area of a Circle
    • 8.4. Exercises
  • 8.5. More Area Relationships in the Circle
    • Area of a Sector
    • Area of a Segment
    • Area of a Triangle with an Inscribed Circle
    • 8.5. Exercises
    • Perspective on History: Sketch of Pythagoras
    • Perspective on Applications: Another Look at the Pythagorean Theorem
  • Summary
  • Overview
  • Review Exercises
  • Chapter 8 Test
• 9. Surfaces and Solids
  • 9.1. Prisms, Area, and Volume
    • Prisms
    • Area of a Prism
    • Volume of a Prism
    • 9.1. Exercises
  • 9.2. Pyramids, Area, and Volume
    • Surface Area of a Pyramid
    • Volume of a Pyramid
    • 9.2. Exercises
  • 9.3. Cylinders and Cones
    • Cylinders
    • Surface Area of a Cylinder
    • Volume of a Cylinder
    • Cones
    • Surface Area of a Cone
    • Volume of a Cone
    • Solids of Revolution
    • 9.3. Exercises
  • 9.4. Polyhedrons and Spheres
    • Polyhedrons
    • Regular Polyhedrons
    • Spheres
    • Surface Area of a Sphere
    • Volume of a Sphere
    • 9.4. Exercises
    • Perspective on History: Sketch of René Descartes
    • Perspective on Applications: Birds in Flight
  • Summary
  • Overview
  • Review Exercises
  • Chapter 9 Test
• 10. Analytic Geometry
  • 10.1. The Rectangular Coordinate System
    • The Distance Formula
    • The Midpoint Formula
    • Proof of the Midpoint Formula (Optional)
    • 10.1. Exercises
  • 10.2. Graphs of Linear Equations and Slope
    • The Graph of an Equation
    • The Slope of a Line
    • 10.2. Exercises
  • 10.3. Preparing to Do Analytic Proofs
    • 10.3. Exercises
  • 10.4. Analytic Proofs
    • 10.4. Exercises
  • 10.5. Equations of Lines
    • Slope-Intercept Form of a Line
    • Point-Slope Form of a Line
    • Solving Systems of Equations
    • 10.5. Exercises
  • 10.6. The Three-Dimensional Coordinate System
    • Points
    • Lines
    • The Distance Formula
    • The Midpoint Formula
    • Planes
    • Line and Plane Relationships
    • Intersection of Planes
    • Spheres
    • 10.6. Exercises
    • Perspective on History: The Banach-Tarski Paradox
    • Perspective on Applications: The Point-of-Division Formulas
  • Summary
  • Review Exercises
  • Chapter 10 Test
• 11. Introduction to Trigonometry
  • 11.1. The Sine Ratio and Applications
    • 11.1. Exercises
  • 11.2. The Cosine Ratio and Applications
    • 11.2. Exercises
  • 11.3. The Tangent Ratio and Other Ratios
    • 11.3. Exercises
  • 11.4. Applications with Acute Triangles
    • Area of a Triangle
    • Law of Sines
    • Law of Cosines
    • 11.4. Exercises
    • 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
• Formulas
• Abbreviations
• Symbols
• Common Variables

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