Elementary Geometry for college students (5th ed)

1. Line and Angle Relationships

1.1 Sets, Statements, and Reasoning

1.2 Informal Geometry and Measurement

1.3 Early Definitions and Postulates

1.4 Angles and Their Relationships

1.5 Introduction to Geometric Proof

1.6 Relationships: Perpendicular Lines

1.7 The Formal Proof of a Theorem

Perspective on History: The Development of Geometry

Perspective on Application: Patterns

Chapter 1 Summary

Chapter 1 Review Exercises

Chapter 1 Test

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 Application: Non-Euclidean Geometries

Chapter 2 Summary

Chapter 2 Review Exercises

Chapter 2 Test

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 Application: Pascal’s Triangle

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Test

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 Application: Square Numbers as Sums

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Test

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’s Proof

Perspective on Application: An Unusual Application of Similar Triangles

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Test

6. Circles

6.1 Circles and Related Segments and Angles

6.2 More Angle Measures in the Circle

6.3 Line and Segment Relationships in the Circle

6.4 Some Constructions and Inequalities for the Circle

Perspective on History: Circumference of the Earth

Perspective on Application: Sum of the Interior Angles of a Polygon

Chapter 6 Summary

Chapter 6 Review Exercises

Chapter 6 Test

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 $\pi$

Perspective on Application: The Nine-Point Circle

Chapter 7 Summary

Chapter 7 Review Exercises

Chapter 7 Test

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 Application: Another Look at the Pythagorean Theorem

Chapter 8 Summary

Chapter 8 Review Exercises

Chapter 8 Test

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 René Descartes

Perspective on Application: Birds in Flight

Chapter 9 Summary

Chapter 9 Review Exercises

Chapter 9 Test

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

Perspective on History: The Banach–Tarski Paradox

Perspective on Application: The Point-of-Division Formulas

Chapter 10 Summary

Chapter 10 Review Exercises

Chapter 10 Test

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 Application: Radian Measure of Angles

Chapter 11 Summary

Chapter 11 Review Exercises

Chapter 11 Test

Appendices

Appendix A. Algebra Review

Appendix B. Summary of Constructions, Postulates, Theorems, and Corollaries

Answers

Selected Exercises and Proofs

Glossary

Index