Elementary Geometry for College Students

by Alexander, Daniel C.; Koeberlein, Geralyn M.

• ISBN13: 9780618645251
• ISBN10: 061864525X
• Edition: 4th
• Format: Hardcover
• Copyright: 2006-01-10
• Publisher: Brooks Cole

Summary

Building on the success of its first three editions, the Fourth Edition of this market-leading text covers the important principles and real-world applications of plane geometry, with additional chapters on solid geometry, analytic geometry, and an introduction to trigonometry. Strongly influenced by both NCTM and AMATYC standards, the text takes an inductive approach that includes integrated activities and tools to promote hands-on application and discovery. New! Tables provide visual connections between figures and concepts and help students better assess their level of mastery and test readiness. New! Chapter Tests have been added to the end of every chapter. New! Proofs have been varied to include written and visual proofs, as well as comparisons, to support students with different learning styles. New! Exercise sets in the Student Study Guide, with cross-references to the text, offer additional practice and review. New! Technology-related margin features encourage the use of the Geometer's Sketchpad, graphing calculators, and further explorations. New! Coverage now includes Section 2.6, Symmetry and Transformations. New! Technology Package includes mathSpace tutorial CD and the HM ClassPrep CD with computerized test bank. Updated! The number of Exercises and Explorations has been increased. Highly visual approach begins with the presentation of an idea, followed by the examination and development of a theory, verification of the theory through deduction, and finally, application of the principles to the real world. Discovery features reinforce the text's inductive approach: activities integrated throughout enable students to discover geometry concepts on their own, and section tools provide with hands-on application of geometric concepts Applications reinforce the connection of geometry to the real world: high-interest Chapter Openers introduce the principal notion of the chapter and relate to the real world and A Perspective On... sections conclude each chapter, providing sketches that are interesting, sometimes historical, and always informative. Summaries of constructions, postulates, and theorems are provided, and an easy-to-navigate numbering system for postulates and theorems provides a user-friendly structure. In response to user feedback, paragraph proofs feature more prominently in this edition. Comprehensive appendices include Algebra Review and An Introduction to Logic. A glossary of terms, a summary of applications in the text, and selected answers are also provided in the back of the text.

Table of Contents

Preliminary Contents

Line and Angle Relations

Sets, statements and reasoning

Informal geometry and measurement

Early definitions and postulates

Angles and their relationships

Introduction to geometric proof

Relationships: perpendicular lines

The formal proof of a theorem

Parallel Lines

The parallel postulate and special angles

Indirect proof

Proving lines parallel

The angles of a triangle

Convex polygons

Symmetry and transformations

Triangles

Congruent triangles

Corresponding parts of congruent triangles

Isosceles triangles

Basic constructions justified

Inequalities in a triangle

Quadrilaterals

Properties of a parallelogram

The parallelogram and kite

The rectangle, square, and rhombus

The trapezoid

Similar Triangles

Ratios, Rates, and Proportions

Similar Polygons

Proving Triangles Similar

The Pythagorean Theorem

Special Right Triangles

Segments Divided Proportionately

Circles

Circles and Related Segments and Angles

More Angle Relationships in the Circle

Line and Segment Relationships in the Circle

Some Constructions and Inequalities for the Circle

Locus of Points

Concurrence of Lines

Areas of Polygons and Circles

Area and initial postulates

Perimeter and area of polygons

Regular polygons and area

Circumference and area of a circle

More area relationships in the circle

Surfaces and Solids

Prisms, area, and volume

Pyramids, area, and volume

Cylinders and cones

Polyhedrons and spheres

Analytic Geometry

The Rectangular Coordinate System

Graphs of Linear Equations and Slope

Preparing to do Analytic Proofs

Analytic Proofs

Equations of Lines

Introduction to Trigonometry

The Sine Ratio and Applications

The Cosine Ratio and Applications

The Tangent Ratio and Other Ratios

Applications to Acute Triangles

Table of Contents provided by Publisher. All Rights Reserved.