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9780471799405

Geometry Workbook For Dummies

by
  • ISBN13:

    9780471799405

  • ISBN10:

    0471799408

  • Edition: 1st
  • Format: Paperback
  • Copyright: 2006-11-06
  • Publisher: For Dummies

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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

Supplemental Materials

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