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# Geometry Fundamental Concepts and Applications

**by**Bass, Alan

### 9780321473318

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## Summary

## 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

Preface | p. V |

A Brief History of Geometry | p. 1 |

Basic Geometry Concepts | p. 3 |

An Overview of This Supplement | p. 3 |

Points, Lines, and Planes | p. 3 |

Between Points | p. 6 |

Congruent Objects and Bisectors | p. 8 |

Solving Word Problems in Geometry | p. 10 |

Construction Example: Using a Straightedge and Compass to Bisect a Line Segment | p. 11 |

The History of Geometry | p. 17 |

More About Angles | p. 19 |

Measuring and Classifying Angles | p. 19 |

Notation for Angle Measure and Congruence | p. 21 |

Common Relationships between Angles | p. 22 |

Parallel Lines Cut by a Transversal | p. 27 |

Construction Example: Using a Straightedge and Compass to Bisect an Angle | p. 29 |

Proofs in Geometry | p. 35 |

Triangles | p. 37 |

The Practical Nature of Triangles | p. 37 |

Classifying Triangles | p. 38 |

The Angles of a Triangle | p. 41 |

Right Triangles: The Pythagorean Theorem | p. 44 |

Comparing the Sides and Angles of a Triangle | p. 45 |

Construction Example: Using a Compass to Create an Equilateral Triangle | p. 46 |

Proofs in Geometry | p. 52 |

More About Triangles-Congruence and Similarity | p. 55 |

Congruent Triangles | p. 55 |

Congruence Theorems for Triangles | p. 56 |

Similar Triangles | p. 57 |

Special Right Triangles | p. 61 |

Finding the Height of a Building | p. 70 |

Quadrilaterals | p. 71 |

Classifying Quadrilaterals | p. 71 |

The Angles of a Quadrilateral | p. 75 |

Diagonals | p. 75 |

Quadrilaterals and Bisectors | p. 81 |

Polygons | p. 83 |

Identifying and Classifying Polygons | p. 83 |

Theorems Concerning the Angles and Diagonals of a Polygon | p. 85 |

Dissecting a Regular Hexagon | p. 91 |

Area and Perimeter | p. 93 |

Perimeter | p. 93 |

Area | p. 95 |

Derived Area Formulas | p. 96 |

Your Dream House | p. 108 |

Circles | p. 109 |

Definitions and Terminology | p. 109 |

Circumference and Area | p. 112 |

Sectors and Arc Length | p. 114 |

Proofs in Geometry | p. 122 |

Volume and Surface Area | p. 125 |

Volume Formulas for Cubes, Rectangular Solids, Cylinders, and Prisms | p. 126 |

The Sphere | p. 129 |

Cones and Pyramids | p. 129 |

Surface Area | p. 130 |

Approximating Volumes | p. 139 |

Trigonometry | p. 141 |

Terminology Associated with Ratios in a Right Triangle | p. 141 |

Finding Unknown Values | p. 143 |

Trigonometric Ratio Values for Special Angles | p. 146 |

Trig Meets World | p. 151 |

Glossary | p. 153 |

Solutions to Odd-Numbered Exercises | p. 157 |

Index | p. 163 |

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