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Building on the success of its first five editions, the Sixth Edition of the market-leading text explores the important principles and real-world applications of plane, coordinate, and solid geometry. Strongly influenced by both NCTM and AMATYC standards, the text includes intuitive, inductive, and deductive experiences in its explorations. Goals of the authors for the students include a comprehensive development of the vocabulary of geometry, an intuitive and inductive approach to development of principles, and the strengthening of deductive skills that leads to both verification of geometric theories and the solution of geometry-based real world applications. Updates in this edition include the addition of 150 new problems, new applications, new Discover! activities and examples and additional material on select topics such as parabolas and a Three-Dimensional Coordinate System.
Daniel C. Alexander, now retired, taught mathematics at the secondary and college levels for over 40 years. His final 25 years of teaching were at Parkland College in Champaign, Illinois; before retirement, his position at Parkland College was as mathematics professor emeritus. Although Professor Alexander held undergraduate and graduate degrees from Southern Illinois University, he also completed considerable post graduate course work as well. He delivered many talks and participated in various panel discussions at mathematics conferences of IMACC, AMATYC, and ICTM. Further, he had numerous published articles in the ICTM, NCTM,and AMATYC mathematics journals.
Geralyn M. Koeberlein, now retired, taught mathematics at Mahomet-Seymour High School in Mahomet, Illinois for 34 years. She taught several levels of math, from Algebra I to AB Calculus. In the last few years of her career, Geralyn was also Chair of the Math and Science Department. After receiving her Master's Degree from the University of Illinois early in her teaching years, Geralyn continued her education by receiving over 90 hours of post graduate credit. She was a member of the the ICTM and the NCTM.
Chapter 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: Perpindicular Lines 1.7 The Formal Proof of a Theorem PERSPECTIVE ON HISTORY: The Development of Geometry PERSPECTIVE ON APPLICATION: Patterns Summary Review Exercises Chapter 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 APPLICATION: Non-Euclidean Geometries Summary Review Exercises Chapter Test Chapter 3 Triangles 3.1 Congruent Triangles 3.2 Correspondening 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 Summary Review Exercises Chapter 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 APPLICATION: Square Numbers as Sums Summary Review Exercises Chapter Test Chapter 5 Similar Triangles 5.1 Ratios, Rates and Proportions 5.2 Similar Polygons 5.3 Proving Triangles Similar 5.4 The Pythagorean Theory 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 Summary Review Exercises Chapter Test Chapter 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 Construction and Inequalities in the Circle PERSPECTIVE ON HISTORY: Circumference of the Earth PERSPECTIVE ON APPLICATION: Sum of the Interior Angles of a Polygon Summary Review Exercises Chapter 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 π (Pi) PERSPECTIVE ON APPLICATION: The Nine-Point Circle Summary Review Exercises Chapter Test Chapter 8 Areas of Polygons and Circles 8.1 Areas 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 Summary Review Exercises Chapter 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 APPLICATION: Birds in Flight Summary Review Exercises Chapter Test Chapter 10 Analytical 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 A Three-Dimensional Coordinate System PERSPECTIVE ON HISTORY: The Banach-Tarski Paradox PERSPECTIVE ON APPLICATION: The Point-of-Division Formulas Summary Review Exercises Chapter 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 APPLICATION: Radian Measure of Angles Summary Review Exercises Chapter Test Appendix A: Algebra Review Appendix B: Summaries of Constructions, Postulates, Theorems, and Corollaries Answers Glossary Index
This is a great text. I've read some reviews at other sites, claiming that this has to be the worse textbook ever written. Well, I'm here to tell you that those are false statements. This book, is not like your typical high school geometry text. It was clearly written in mind for college student, therefore it is a tad bit more challenging. One has to remember that geometry is all about proofs, not just the figures/shapes. So if you're buying this book for a class or for your own pleasure, be ready to test you reasoning skills. Nevertheless this is a rigorous yet concisely written textbook. And remember, it's all about the logic.
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