Higher Education

Elementary Geometry for College Students, 6th Edition

  • Daniel C. Alexander Parkland College
  • Geralyn M. Koeberlein Mahomet-Seymour High School
  • ISBN-10: 1285195698  |  ISBN-13: 9781285195698
  • 624 Pages
  • Previous Editions: 2011, 2007, 2003
  • © 2015 | Published
  • College Bookstore Wholesale Price = $212.25

About

Overview

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.

Features and Benefits

  • Proofs include written and visual proofs, as well as comparisons, to support students with different learning styles.
  • Technology-related margin features encourage the use of the Geometer’s Sketchpad, graphing calculators, and further explorations.
  • Reminders found in the margin serve as a convenient recall mechanism.
  • Discover! activities emphasize induction in the development of geometry.
  • Geometry in Nature and Geometry in the Real World emphasize examples of geometry found in everyday life.
  • Tables found in chapter endmatter that emphasize chapter properties such as those for triangles, quadrilaterals, circles provide visual connections between figures and concepts and help students better assess their level of mastery and test readiness.
  • Index of Applications calls attention to the practical applications of geometry.
  • Warnings are provided so that students might avoid common pitfalls studying geometry.
  • Perspective on History provides a glimpse of the history of geometry.
  • Perspective on Application provides illustrations of geometry in practice.
  • Chapter Summaries review the chapter, preview the chapter to follow, and provide a list of important concepts found in the current chapter.
  • Chapter Reviews and Tests provide numerous practice problems and tests for each chapter.
  • Exercise sets in the Student Study Guide, with cross-references to the text, offer additional practice and review.

Table of Contents

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 René 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

What's New

  • Approximately 150 new exercises have been added, many of a challenging nature.
  • New Discover! activities
  • New examples to provide a smoother transition within the revelant section as well as to better prepare students for the exercise set that follows
  • New and updated applications including: -checking for the squareness of the opening of a patio door -the ideal viewer-distance to TV sets of various screen sizes -checking for accuracy in the construction of a garden gazebo -the application of drywall in new construction or remodeling
  • A new section (Section 10.6)on a Three-Dimensional Coordinate System

Supplements

All supplements have been updated in coordination with the main title. Select the main title's "About" tab, then select "What's New" for updates specific to title's edition.

For more information about these supplements, or to obtain them, contact your Learning Consultant.

Instructor Supplements

Cengage Learning Testing, powered by Cognero Instant Access Elementary Geometry  (ISBN-10: 1285979974 | ISBN-13: 9781285979977)

Student Study Guide with Solutions Manual  (ISBN-10: 1285196813 | ISBN-13: 9781285196817)

This guide provides worked-out solutions to select odd-numbered problems from the text as well as new Interactive Exercise sets for additional review. Solutions for the additional Interactive Exercise sets are provided on the Instructor Website.

List Price = $104.95  | CengageBrain Price = $104.95  | College Bookstore Wholesale Price = $78.75

Student Supplements

Student Study Guide with Solutions Manual  (ISBN-10: 1285196813 | ISBN-13: 9781285196817)

This guide provides worked-out solutions to select odd-numbered problems from the text as well as new Interactive Exercise sets for additional review. Solutions for the additional Interactive Exercise sets are provided on the Instructor Website.

List Price = $104.95  | CengageBrain Price = $104.95  | College Bookstore Wholesale Price = $78.75

Meet the Author

Author Bio

Daniel C. Alexander

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

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.