Geometry Workbook For Dummies

by Ryan, Mark

• ISBN13: 9780471799405
• ISBN10: 0471799408
• Edition: 1st
• Format: Paperback
• Copyright: 2006-11-06
• Publisher: For Dummies

Summary

From proofs to polygons -- solve geometry problems with ease Got a grasp on the terms and concepts you need to know, but get lost halfway through a problem or worse yet, not know where to begin? No fear -- this hands-on guide focuses on helping you solve the many types of geometry problems you encounter in a focused, step-by-step manner. With just enough refresher explanations before each set of problems, you'll sharpen your skills and improve your performance. You'll see how to work with proofs, theorems, triangles, circles, formulas, 3-D figures, and more! * 100s of Problems! * Step-by-step answer sets clearly identify where you went wrong (or right) with a problem * Get the inside scoop on geometry shortcuts and strategies * Know where to begin and how to solve the most common problems * Use geometry in practical applications with confidence

Author Biography

Mark Ryan, a graduate of Brown University and the University of Wisconsin Law School, has been teaching math since 1989. He runs the Math Center in Winnetka, Illinois (www.themathcenter.com), where he teaches high school math courses including an introduction to geometry and a workshop for parents based on a program he developed, The 10 Habits of Highly Successful Math Students. In high school, he twice scored a perfect 800 on the math portion of the SAT, and he not only knows mathematics, he has a gift for explaining it in plain English. He practiced law for four years before deciding he should do something he enjoys and use his natural talent for mathematics. Ryan is a member of the Authors Guild and the National Council of Teachers of Mathematics.
Geometry Workbook For Dummies is Ryan’s fourth book. Everyday Math for Everyday Life was published in 2002, Calculus For Dummies (Wiley) in 2003, and Calculus Workbook For Dummies in 2005. His math books have sold over 100,000 copies.

Table of Contents

Introduction	1	(1)
About This Book	1	(1)
Conventions Used in This Book	2	(1)
How to Use This Book	2	(1)
Foolish Assumptions	2	(1)
How This Book Is Organized	3	(1)
Part I: Getting Started	3	(1)
Part II: Triangles	3	(1)
Part III: Polygons	3	(1)
Part IV: Circles	4	(1)
Part V: 3-D Geometry and Coordinate Geometry	4	(1)
Part VI: The Part of Tens	4	(1)
Icons Used in This Book	4	(1)
Where to Go from Here	5	(2)
Part I: Getting Started	7	(42)
Introducing Geometry and Geometry Proofs!	9	(10)
Making the Right Assumptions: What Is Geometry?	9	(3)
If-Then Logic: If You Bought This Book, Then You Must Love Geometry!	12	(2)
Discovering Geometry Proofs	14	(3)
Solutions for Introducting Geometry and Geometry Proofs!	17	(2)
Points, Segments, Lines, Rays, and Angles	19	(30)
Basic Definitions	19	(1)
Union and Intersection Problems	20	(2)
Division in the Ranks: Bisection and Trisection	22	(2)
Perfect Hilarity for Perpendicularity	24	(2)
You Complete Me: Complementary and Supplementary Angles	26	(4)
Adding and Subtracting Segments and Angles	30	(3)
Multiplying and Dividing Angles and Segments	33	(4)
X Marks the Spot: Using Vertical Angles	37	(2)
Switching It Up with the Transitive and Substitution Properties	39	(3)
Solutions for Points, Segments, Lines, Rays, and Angles	42	(7)
Part II: Triangles	49	(64)
Triangle Fundamentals and Other Cool Stuff	51	(32)
Triangle Types and Triangle Basics	51	(4)
Altitudes, Area, and the Super Hero Formula	55	(3)
Balancing Things Out with Medians and Centroids	58	(1)
Three More ``Centers'' of a Triangle	59	(5)
The Pythagorean Theorem	64	(3)
Pythagorean Triple Triangles	67	(3)
Unique Degrees: Two Special Right Triangles	70	(4)
Solutions for Triangle Fundamentals and Other Cool Stuff	74	(9)
Congruent Triangles	83	(30)
Sizing Up Three Ways to Prove Triangles Congruent	83	(6)
Corresponding Parts of Congruent Triangles Are Congruent (CPCTC)	89	(4)
Isosceles Rules: If Sides, Then Angles: If Angles, Then Sides	93	(3)
Two More Ways to Prove Triangles Congruent	96	(3)
The Two Equidistance Theorems	99	(5)
Solutions for Congruent Triangles	104	(9)
Part III: Polygons	113	(80)
Quadrilaterals: Your Fine, Four-Sided Friends	115	(36)
Double-Crossers: Transversals and Their Parallel Lines	115	(5)
Quadrilaterals: It's a Family Affair	120	(3)
Properties of the Parallelogram and the Kite	123	(4)
Properties of Rhombuses, Rectangles, and Squares	127	(3)
Properties of Trapezoids and Isosceles Trapezoids	130	(2)
Proving That a Quadrilateral Is a Parallelogram or a Kite	132	(4)
Proving That a Quadrilateral Is a Rhombus, Rectangle, or Square	136	(3)
Solutions for Quadrilaterals: Your Fine, Four-Sided Friends	139	(12)
Area, Angles, and the Many Sides of Polygon Geometry	151	(14)
Square Units: Finding the Area of Quadrilaterals	151	(4)
A Standard Formula for the Area of Regular Polygons	155	(2)
More Fantastically Fun Polygon Formulas	157	(3)
Solutions for Area, Angles, and the Many Sides of Polygon Geometry	160	(5)
Similarity: Size Doesn't Matter	165	(28)
Defining Similarity: The Sincerest Flattery	165	(3)
Proving Triangles Similar	168	(4)
Corresponding Sides and CSSTP --- Cats Stalk Silently Then Pounce	172	(3)
Similar Rights: The Altitude-on-Hypotenuse Theorem	175	(3)
Three More Theorems Involving Proportions	178	(5)
Solutions for Similarity: Size Doesn't Matter	183	(10)
Part IV: Circles	193	(34)
Circular Reasoning	195	(16)
The Segments Within: Radii and Chords	195	(4)
Introducing Arcs, Chords, and Central Angles	199	(3)
Touching on Radii and Tangents	202	(4)
Solutions for Circular Reasoning	206	(5)
Scintillating Circle Formulas	211	(16)
Not Quite Coming Full Circle: Area and ``Perimeter'' of Circles, Sectors, and Segments	211	(3)
Angles, Circles, and Their Connections: The Angle-Arc Theorems and Formulas	214	(3)
The Power Theorems That Be	217	(4)
Solutions for Scintillating Circle Formulas	221	(6)
Part V: 3-D Geometry and Coordinate Geometry	227	(58)
2-D Stuff Standing Up	229	(14)
Lines Perpendicular to Planes: They're All Right	229	(4)
Parallel, Perpendicular, and Intersecting Lines and Planes	233	(5)
Solutions for 2-D Stuff Standing Up	238	(5)
Solid Geometry: Digging into Volume and Surface Area	243	(14)
Starting with Flat-Top Figures	243	(3)
Sharpening Your Skills with Pointy-Top Figures	246	(3)
Rounding Out Your Understanding with Spheres	249	(2)
Solutions for Solid Geometry	251	(6)
Coordinate Geometry, Courtesy of Descartes	257	(14)
Formulas, Schmormulas: Slope, Distance, and Midpoint	257	(3)
Mastering Coordinate Proofs with Algebra	260	(1)
Using the Equations of Lines and Circles	261	(3)
Solutions for Coordinate Geometry, Courtesy of Descartes	264	(7)
Transforming the (Geometric) World: Reflections, Rotations, and Translations	271	(14)
Reflections on Mirror Images	271	(3)
Les Transformations Geometriques	274	(2)
So You Say You Want a ... Rotation?	276	(2)
Working with Glide Reflections	278	(3)
Solutions for Transforming the World	281	(4)
Part VI: The Part of Tens	285	(10)
Ten (Plus) Incredibly Fantastic Strategies for Doing Proofs	287	(4)
Look for Congruent Triangles	287	(1)
Try to Find Isosceles Triangles	287	(1)
Look for Radii, and Draw More Radii	288	(1)
Look for Parallel Lines	288	(1)
Make a Game Plan	288	(1)
Use All the Givens	288	(1)
Check Your If-Then Logic	288	(1)
Work Backwards	289	(1)
Make Up Numbers for Segments and Angles	289	(1)
Think Like a Computer	289	(1)
Bonus! Number 11 (Like the Amp in Spinal Tap That Goes Up to 11): Do Something!	290	(1)
Ten Things You Better Know (for Geometry), or Your Name Is Mudd	291	(4)
The Pythagorean Theorem (the Queen of All Geometry Theorems)	291	(1)
Special Right Triangles	291	(1)
Area Formulas	292	(1)
Sum of Angles	292	(1)
Circle Formulas	292	(1)
Angle-Arc Theorems	292	(1)
Power Theorems	293	(1)
Coordinate Geometry Formulas	293	(1)
Volume Formulas	293	(1)
Surface Area Formulas	294	(1)
Index	295