Elementary Geometry for College Students / Edition 2by Daniel C. Alexander, Geralyn M. Koeberlein
Pub. Date: 11/28/1998
Publisher: Houghton Mifflin Company College Division
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… See more details below
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 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, 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.
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Table of ContentsContents
Note: Each chapter concludes with a Summary, Review Exercises, and a Chapter Test.
- 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
- 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-Euclidian Geometrics
- 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
- 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
- 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 Proportionately
- Perspective on History: Ceva's Proof
- Perspective on Application: An UnusualApplication of Similar Triangles
- 6. Circles
- 6.1 Circles and Related Segments and Angles
- 6.2 More Angle Relationships in the Circle
- 6.3 Line and Segment Relationships in the Circle
- 6.4 Some Constructions and Inequalities for the Circle
- 6.5 Locus of Points
- 6.6 Concurrence of Lines
- Perspective on History: The Value of π
- Perspective on Application: The Nine-Point Circle
- 7. Areas of Polygons and Circles
- 7.1 Area and Initial Postulates
- 7.2 Perimeter and Area of Polygons
- 7.3 Regular Polygons and Area
- 7.4 Circumference and Area of a Circle
- 7.5 More Area Relationships in the Circle
- Perspective on History: Sketch of Pythagoras
- Perspective on Application: Another Look at the Pythagorean Theorem
- 8. Surfaces and Solids
- 8.1 Prisms, Area, and Volume
- 8.2 Pyramids, Area, and Volume
- 8.3 Cylinders and Cones
- 8.4 Polyhedrons and Spheres
- Perspective on History: Sketch of René Descartes
- Perspective on Application: Birds in Flight
- 9. Analytic Geometry
- 9.1 The Rectangular Coordinate System
- 9.2 Graphs of Linear Equations and Slope
- 9.3 Preparing to Do Analytic Proofs
- 9.4 Analytic Proofs
- 9.5 Equations of Lines
- Perspective on History: The Banach-Tarski Paradox
- Perspective on Application: The Point-of-Division
- 10. Introduction to Trigonometry
- 10.1 The Sine Ratio and Applications
- 10.2 The Cosine Ratio and Applications
- 10.3 The Tangent Ratio and Other Ratios
- 10.4 Applications to Acute Triangles
- Perspective on History: Sketch of Plato
- Perspective on Application: Radian Measuer of Angles
- A. Algebra Review
- B. Summary of Constructions, Postulates, and Theorems and Corollaries
- Selected Exercises and Proofs
- 1.1 Sets, Statements, and Reasoning
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