Geometry Fundamental Concepts and Applications

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  • Edition: 1st
  • Format: Paperback
  • Copyright: 2007-04-19
  • Publisher: Pearson

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This Geometry workbook makes the fundamental concepts of geometry accessible and interesting for college students and incorporates a variety of basic algebra skills in order to show the connection between Geometry and Algebra. Topics include: A Brief History of Geometry 1. Basic Geometry Concepts 2. More about Angles 3. Triangles 4. More about Triangles: Similarity and Congruence 5. Quadrilaterals 6. Polygons 7. Area and Perimeter 8. Circles 9. Volume and Surface Area 10. Basic Trigonometry

Author Biography

Alan Bass earned his Master of Science degree in Mathematics from the University of North Carolina at Wilmington. Presently, he lives, writes, runs, swims, bikes, hikes, and plays music with his wife Holly in sunny San Diego, CA. (He also enjoys fine wine and all things nerdy). He is an Associate Professor of Mathematics at San Diego Mesa College (just got tenure) and has been teaching developmental math for more than ten years. He is a big advocate for math study skills so, through a grant project called Pathways through Algebra, he got into networking with other schools to make study skills programs happen. He has worked on developing learning communities, establishing curriculum and pedagogy for study skills classes, and methods for incorporating study skills directly into the classroom. He has created and accumulated a ton of material, and wants to share it with you! For more information, check out his website at http://www.pearsonhighered.com/alanbass/index.html .

Table of Contents

Prefacep. V
A Brief History of Geometryp. 1
Basic Geometry Conceptsp. 3
An Overview of This Supplementp. 3
Points, Lines, and Planesp. 3
Between Pointsp. 6
Congruent Objects and Bisectorsp. 8
Solving Word Problems in Geometryp. 10
Construction Example: Using a Straightedge and Compass to Bisect a Line Segmentp. 11
The History of Geometryp. 17
More About Anglesp. 19
Measuring and Classifying Anglesp. 19
Notation for Angle Measure and Congruencep. 21
Common Relationships between Anglesp. 22
Parallel Lines Cut by a Transversalp. 27
Construction Example: Using a Straightedge and Compass to Bisect an Anglep. 29
Proofs in Geometryp. 35
Trianglesp. 37
The Practical Nature of Trianglesp. 37
Classifying Trianglesp. 38
The Angles of a Trianglep. 41
Right Triangles: The Pythagorean Theoremp. 44
Comparing the Sides and Angles of a Trianglep. 45
Construction Example: Using a Compass to Create an Equilateral Trianglep. 46
Proofs in Geometryp. 52
More About Triangles-Congruence and Similarityp. 55
Congruent Trianglesp. 55
Congruence Theorems for Trianglesp. 56
Similar Trianglesp. 57
Special Right Trianglesp. 61
Finding the Height of a Buildingp. 70
Quadrilateralsp. 71
Classifying Quadrilateralsp. 71
The Angles of a Quadrilateralp. 75
Diagonalsp. 75
Quadrilaterals and Bisectorsp. 81
Polygonsp. 83
Identifying and Classifying Polygonsp. 83
Theorems Concerning the Angles and Diagonals of a Polygonp. 85
Dissecting a Regular Hexagonp. 91
Area and Perimeterp. 93
Perimeterp. 93
Areap. 95
Derived Area Formulasp. 96
Your Dream Housep. 108
Circlesp. 109
Definitions and Terminologyp. 109
Circumference and Areap. 112
Sectors and Arc Lengthp. 114
Proofs in Geometryp. 122
Volume and Surface Areap. 125
Volume Formulas for Cubes, Rectangular Solids, Cylinders, and Prismsp. 126
The Spherep. 129
Cones and Pyramidsp. 129
Surface Areap. 130
Approximating Volumesp. 139
Trigonometryp. 141
Terminology Associated with Ratios in a Right Trianglep. 141
Finding Unknown Valuesp. 143
Trigonometric Ratio Values for Special Anglesp. 146
Trig Meets Worldp. 151
Glossaryp. 153
Solutions to Odd-Numbered Exercisesp. 157
Indexp. 163
Table of Contents provided by Ingram. All Rights Reserved.

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