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Elementary Geometry for College Students

by: Alexander,Daniel C.

ISBN: 9780618645251 | 061864525X

Edition: 4th
Format: Hardcover
Publisher: Cengage Learning
Pub. Date: 1/10/2006

Newer Edition Available

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Summary Table of Contents

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... MORE 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 the HM ClassPrep CD with computerized test bank (powered by Diploma)."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, andsection tools provide with hands-on application of geometric conceptsApplications 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.

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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.

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Elementary Geometry for College Students

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