## Master Math: Geometry (Master Math Series)

### Debra Anne Ross

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Master Math: Geometry and the Master Math series as a whole are clear, concise, and yet comprehensive reference sources. They are designed to allow quick access to clearly presented and easy-to-understand explanations of concepts, principles, definitions, examples, and applications. This book was written for students, teachers, tutors, and parents, as well as for scientists and engineers who need to look up principles, definitions, explanations of concepts, and pertinent examples. It provides everything a high school or first year college student needs to know including: explanation of deductive reasoning, how to perform proofs, definitions, theorems, and postulates, Examples pertaining to points, lines, plans, angles, and ratios, coverage on triangles, quadrilaterals, polygons, and much more!

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Debra Anne Ross has a double BA in Chemistry and Biology from the University of California, Santa Cruz, and and MS in Chemical Engineering from Stanford University. Debra's career encompasses biology, chemistry, biochemistry, engineering, biosensors, pharmaceutical drug discovery, and intellectual property. She is the author of the popular Master Math books, The 3:00 PM Secret: Live Slim and Strong Live Your Dreams, The 3:00 PM Secret: Ten Day Dream Diet (2009), and Arrows Through Time: A Time Travel Tale of Adventure, Courage, and Faith (2009).

TABLE OF CONTENTS Introduction CHAPTER 1: Deductive Reasoning and Proofs 1.1. The language of geometry 1.2. Deductive reasoning 1.3. Theorems and how to write a proof 1.4. Key axioms and postulates 1.5. Chapter 1 summary and highlights CHAPTER 2: Points, Lines, Planes, and Angles 2.1. Points, lines, and planes 2.2. Line segments and distance 2.3. Parallel lines 2.4. Perpendicular lines 2.5. Distances and bisectors 2.6. Rays and angles 2.7. Chapter 2 summary and highlights CHAPTER 3: Ratios and Proportions 3.1. Ratios and proportions 3.2. Proportional segments 3.3. Chapter 3 summary and highlights CHAPTER 4: Triangles, Congruence, and Similarity 4.1. Triangle definitions, interior angle sum, and exterior angles 4.2. Types of triangles 4.3. Parts of triangles, altitude, bisector, median, and Ceva’s Theorem 4.4. Inequalities and triangles 4.5. Congruent triangles 4.6. Similar triangles: Congruent angles and sides in proportion 4.7. Similar right triangles 4.8. Right triangles: Pythagorean Theorem and 30°:60°:90° and 45°:45°:90° triangles 4.9. Triangles and trigonometric functions 4.10. Area of a triangle 4.11. Chapter 4 summary and highlights CHAPTER 5: Polygons and Quadrilaterals 5.1. Polygons 5.2. Sum of the interior and exterior angles in a polygon 5.3. Regular polygons and their interior and exterior angle measures 5.4. Quadrilaterals 5.5. Parallelograms 5.6. Special parallelograms: Rectangles, rhombuses, and squares 5.7. Trapezoids 5.8. Area and perimeter of squares, rectangles, parallelograms, rhombuses, trapezoids, other polygons, and regular polygons 5.9. Congruence, area, and similarity 5.10. Chapter 5 summary and highlights CHAPTER 6: Circles 6.1. Circles: Definitions 6.2. Arcs, central angles, and inscribed angles 6.3. Chords, arcs, and angles 6.4. Secants, angles, arcs, and segments 6.5. Tangents 6.6. Circumference and area of circles and sectors 6.7. Circumscribed and inscribed polygons 6.8. Chapter 6 summary and highlights CHAPTER 7: Geometric Solids: Surface Area and Volume

of Three-Dimensional Objects 7.1. Solids 7.2. Prisms: Cubes, rectangular solids, and oblique and right prisms 7.3. Pyramids 7.4. Cylinders 7.5. Cones 7.6. Spheres 7.7. Similar solids 7.8. Cavalieri’s principle 7.9. Chapter 7 summary and highlights CHAPTER 8: Constructions and Loci 8.1. Introduction 8.2. Constructions involving lines and angles 8.3. Constructions involving triangles 8.4. Constructions involving circles and polygons 8.5. Construction involving area 8.6. Locus of points 8.7. Chapter 8 summary and highlights CHAPTER 9: Coordinate or Analytic Geometry 9.1. Rectangular coordinate systems: Definitions 9.2. Distance between points 9.3. Midpoint formula 9.4. Slope of a line including parallel and perpendicular lines 9.5. Defining linear equations 9.6. Graphing linear equations 9.7. Chapter 9 summary and highlights Index

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ISBN 10:  1598639846 ISBN 13:  9781598639841
Publisher: Cengage Learning PTR, 2009
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## 1.Master Math: Geometry (Master Math Series) [Jul 28, 2004] Ross, Debra Anne

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