Geometry For Dummies

**Hit the geometry wall? Get up and running with this no-nonsense guide!**Does the thought of geometry make you jittery? You're not alone. Fortunately, this down-to-earth guide helps you approach it from a new angle, making it easier than ever to conquer your fears and score your highest in geometry. From getting started with geometry basics to making friends with lines and angles, you'll be proving triangles congruent, calculating circumference, using formulas, and serving up pi in no time. Geometry is a subject full of mathematical richness and beauty. But it's a subject that bewilders many students because it's so unlike the math they've done before—it requires the use of deductive logic in formal proofs. If you're having a hard time wrapping your mind around what that even means, you've come to the right place! Inside, you'll find out how a proof's chain of logic works and even discover some secrets for getting past rough spots along the way. You don't have to be a math genius to grasp geometry, and this book helps you get un-stumped in a hurry! * Find out how to decode complex geometry proofs * Learn to reason deductively and inductively * Make sense of angles, arcs, area, and more * Improve your chances of scoring higher in your geometry class There's no reason to let your nerves get jangled over geometry—your understanding will take new shape with the help of __Geometry For Dummies__. Title Page......Page 3 Copyright Page......Page 4 Table of Contents......Page 7 About This Book......Page 15 What You’re Not to Read......Page 16 Icons Used in This Book......Page 17 Where to Go from Here......Page 18 Part 1 Getting Started with Geometry Basics......Page 19 Chapter 1 Introducing Geometry......Page 21 Two-dimensional shapes......Page 22 Getting Acquainted with Geometry Proofs......Page 24 Easing into proofs with an everyday example......Page 25 Turning everyday logic into a proof......Page 26 Sampling a simple geometrical proof......Page 27 When you’ll use your knowledge of shapes......Page 28 When you’ll use your knowledge of proofs......Page 29 Why You Won’t Have Any Trouble with Geometry......Page 30 Getting Down with Definitions......Page 31 A Few Points on Points......Page 35 Singling out horizontal and vertical lines......Page 36 Doubling up with pairs of lines......Page 37 Investigating the Plane Facts......Page 39 Goldilocks and the three angles: Small, large, and just “right”......Page 40 Angle pairs: Often joined at the hip......Page 42 Measuring Segments and Angles......Page 45 Measuring segments......Page 46 Measuring angles......Page 47 Adding and Subtracting Segments and Angles......Page 50 Bisecting and trisecting segments......Page 51 Bisecting and trisecting angles......Page 52 Proving (Not Jumping to) Conclusions about Figures......Page 54 Part 2 Introducing Proofs......Page 57 Chapter 4 Prelude to Proofs......Page 59 Getting the Lay of the Land: The Components of a Formal Geometry Proof......Page 60 If-then chains of logic......Page 62 You’ve got your reasons: Definitions, theorems, and postulates......Page 63 Bubble logic for two-column proofs......Page 65 Horsing Around with a Two-Column Proof......Page 66 Chapter 5 Your Starter Kit of Easy Theorems and Short Proofs......Page 69 Doing Right and Going Straight: Complementary and Supplementary Angles......Page 70 Addition theorems......Page 73 Subtraction theorems......Page 77 Like Multiples and Like Divisions? Then These Theorems Are for You!......Page 80 The X-Files: Congruent Vertical Angles Are Out There......Page 83 Pulling the Switch with the Transitive and Substitution Properties......Page 85 Chapter 6 The Ultimate Guide to Tackling a Longer Proof......Page 89 Making a Game Plan......Page 90 Using All the Givens......Page 91 Making Sure You Use If-Then Logic......Page 92 Chipping Away at the Problem......Page 93 Jumping Ahead and Working Backward......Page 95 Filling In the Gaps......Page 97 Writing Out the Finished Proof......Page 98 Part 3 Triangles: Polygons of the Three-Sided Variety......Page 101 Taking In a Triangle’s Sides......Page 103 Scalene triangles: Akilter, awry, and askew......Page 104 Isosceles triangles: Nice pair o’ legs......Page 105 Introducing the Triangle Inequality Principle......Page 106 Sizing Up Triangle Area......Page 108 Scaling altitudes......Page 109 Determining a triangle’s area......Page 110 Balancing on the centroid......Page 114 Finding three more “centers” of a triangle......Page 117 Chapter 8 Regarding Right Triangles......Page 121 Applying the Pythagorean Theorem......Page 122 Perusing Pythagorean Triple Triangles......Page 127 The Fab Four Pythagorean triple triangles......Page 128 Families of Pythagorean triple triangles......Page 130 Getting to Know Two Special Right Triangles......Page 132 The 45°- 45°- 90° triangle — half a square......Page 133 The 30°- 60°- 90° triangle — half of an equilateral triangle......Page 134 Chapter 9 Completing Congruent Triangle Proofs......Page 139 Introducing Three Ways to Prove Triangles Congruent......Page 140 SSS: Using the side-side-side method......Page 141 SAS: Taking the side-angle-side approach......Page 142 ASA: Taking the angle-side-angle tack......Page 145 Defining CPCTC......Page 147 Tackling a CPCTC proof......Page 148 Eying the Isosceles Triangle Theorems......Page 151 AAS: Using the angle-angle-side theorem......Page 153 HLR: The right approach for right triangles......Page 156 Going the Distance with the Two Equidistance Theorems......Page 157 Determining a perpendicular bisector......Page 158 Using a perpendicular bisector......Page 159 Making a Game Plan for a Longer Proof......Page 161 Running a Reverse with Indirect Proofs......Page 163 Part 4 Polygons of the Four-or-More-Sided Variety......Page 167 Chapter 10 The Seven Wonders of the Quadrilateral World......Page 169 Crossing the line with transversals: Definitions and theorems......Page 170 Applying the transversal theorems......Page 171 Working with more than one transversal......Page 174 Meeting the Seven Members of the Quadrilateral Family......Page 175 Looking at quadrilateral relationships......Page 177 Working with auxiliary lines......Page 178 Properties of the parallelogram......Page 180 Properties of the three special parallelograms......Page 184 Properties of the kite......Page 187 Properties of the trapezoid and the isosceles trapezoid......Page 189 Chapter 11 Proving That You Have a Particular Quadrilateral......Page 191 Putting Properties and Proof Methods Together......Page 192 Surefire ways of ID-ing a parallelogram......Page 194 Trying some parallelogram proofs......Page 195 Proving That a Quadrilateral Is a Rectangle, Rhombus, or Square......Page 198 Revving up for rectangle proofs......Page 199 Waxing rhapsodic about rhombus proofs......Page 201 Squaring off with square proofs......Page 202 Proving That a Quadrilateral Is a Kite......Page 203 Calculating the Area of Quadrilaterals......Page 207 Getting behind the scenes of the formulas......Page 208 Trying a few area problems......Page 210 Presenting polygon area formulas......Page 215 Tackling more area problems......Page 216 Using Polygon Angle and Diagonal Formulas......Page 219 Interior and exterior design: Exploring polygon angles......Page 220 Handling the ins and outs of a polygon angle problem......Page 221 Criss-crossing with diagonals......Page 222 Chapter 13 Similarity: Same Shape, Different Size......Page 225 Defining and naming similar polygons......Page 226 How similar figures line up......Page 227 Solving a similarity problem......Page 229 Proving Triangles Similar......Page 231 Tackling an AA proof......Page 232 Using SSS~ to prove triangles similar......Page 233 Working through an SAS~ proof......Page 235 Working through a CASTC proof......Page 236 Taking on a CSSTP proof......Page 237 Splitting Right Triangles with the Altitude-on-Hypotenuse Theorem......Page 238 The side-splitter theorem: It’ll make you split your sides......Page 241 Crossroads: The side-splitter theorem extended......Page 243 The angle-bisector theorem......Page 245 Part 5 Working with Not-So-Vicious Circles......Page 249 Chapter 14 Coming Around to Circle Basics......Page 251 Introducing five circle theorems......Page 252 Working through a proof......Page 253 Using extra radii to solve a problem......Page 254 Three definitions for your mathematical pleasure......Page 257 Six scintillating circle theorems......Page 258 Trying your hand at some proofs......Page 259 Going Off on a Tangent about Tangents......Page 261 Introducing the tangent line......Page 262 The common-tangent problem......Page 263 Taking a walk on the wild side with a walk-around problem......Page 265 Chapter 15 Circle Formulas and Theorems......Page 269 Determining arc length......Page 270 Finding sector and segment area......Page 273 Pulling it all together in a problem......Page 275 Angles on a circle......Page 276 Angles inside a circle......Page 279 Angles outside a circle......Page 280 Keeping your angle-arc formulas straight......Page 283 Striking a chord with the chord-chord power theorem......Page 284 Seeking out the secant-secant power theorem......Page 286 Condensing the power theorems into a single idea......Page 289 Part 6 Going Deep with 3-D Geometry......Page 291 Lines Perpendicular to Planes......Page 293 The four ways to determine a plane......Page 297 Line and plane interactions......Page 298 Flat-Top Figures: They’re on the Level......Page 301 Getting to the Point of Pointy-Top Figures......Page 307 Rounding Things Out with Spheres......Page 313 Part 7 Placement, Points, and Pictures: Alternative Geometry Topics......Page 317 Getting Coordinated with the Coordinate Plane......Page 319 The slope dope......Page 321 Going the distance with the distance formula......Page 324 Meeting each other halfway with the midpoint formula......Page 325 The whole enchilada: Putting the formulas together in a problem......Page 326 Step 1: Drawing a general figure......Page 328 Step 2: Solving the problem algebraically......Page 330 Line equations......Page 332 The standard circle equation......Page 333 Chapter 19 Changing the Scene with Geometric Transformations......Page 337 Some Reflections on Reflections......Page 338 Getting oriented with orientation......Page 339 Finding a reflecting line......Page 340 Not Getting Lost in Translations......Page 342 A translation equals two reflections......Page 343 Finding the elements of a translation......Page 344 Turning the Tables with Rotations......Page 347 Finding the center of rotation and the equations of two reflecting lines......Page 348 A glide reflection equals three reflections......Page 352 Finding the main reflecting line......Page 353 Chapter 20 Locating Loci and Constructing Constructions......Page 357 The four-step process for locus problems......Page 358 Two-dimensional locus problems......Page 359 Three-dimensional locus problems......Page 364 Drawing with the Bare Essentials: Constructions......Page 365 Three copying methods......Page 366 Bisecting angles and segments......Page 369 Two perpendicular line constructions......Page 371 Constructing parallel lines and using them to divide segments......Page 372 Part 8 The Part of Tens......Page 375 The Reflexive Property......Page 377 The Parallel-Line Theorems......Page 378 All Radii of a Circle Are Congruent......Page 379 The Triangle Congruence Postulates and Theorems......Page 380 The Triangle Similarity Postulates and Theorems......Page 381 Eureka! Archimedes’s Bathtub Revelation......Page 383 Determining Pi......Page 384 The Golden Ratio......Page 385 The Circumference of the Earth......Page 386 Projectile Motion......Page 387 Golden Gate Bridge......Page 388 A Soccer Ball......Page 389 Index......Page 391 EULA......Page 411

Hit the geometry wall? Get up and running with this no-nonsense guide!

Does the thought of geometry make you jittery? You're not alone. Fortunately, this down-to-earth guide helps you approach it from a new angle, making it easier than ever to conquer your fears and score your highest in geometry. From getting started with geometry basics to making friends with lines and angles, you'll be proving triangles congruent, calculating circumference, using formulas, and serving up pi in no time.

Geometry is a subject full of mathematical richness and beauty. But it's a subject that bewilders many students because it's so unlike the math they've done before—it requires the use of deductive logic in formal proofs. If you're having a hard time wrapping your mind around what that even means, you've come to the right place! Inside, you'll find out how a proof's chain of logic works and even discover some secrets for getting past rough spots along the way. You don't have to be a math genius to grasp geometry, and this book helps you get un-stumped in a hurry!

• Find out how to decode complex geometry proofs
• Learn to reason deductively and inductively
• Make sense of angles, arcs, area, and more
• Improve your chances of scoring higher in your geometry class

There's no reason to let your nerves get jangled over geometry—your understanding will take new shape with the help of Geometry For Dummies.

Hit the geometry wall? Get up and running with this no-nonsense guide! Does the thought of geometry make you jittery? You're not alone. Fortunately, this down-to-earth guide helps you approach it from a new angle, making it easier than ever to conquer your fears and score your highest in geometry. From getting started with geometry basics to making friends with lines and angles, you'll be proving triangles congruent, calculating circumference, using formulas, and serving up pi in no time. Geometry is a subject full of mathematical richness and beauty. But it's a subject that bewilders many students because it's so unlike the math they've done before—it requires the use of deductive logic in formal proofs. If you're having a hard time wrapping your mind around what that even means, you've come to the right place! Inside, you'll find out how a proof's chain of logic works and even discover some secrets for getting past rough spots along the way. You don't have to be a math genius to grasp geometry, and this book helps you get un-stumped in a hurry! Find out how to decode complex geometry proofs Learn to reason deductively and inductively Make sense of angles, arcs, area, and more Improve your chances of scoring higher in your geometry class There's no reason to let your nerves get jangled over geometry—your understanding will take new shape with the help of Geometry For Dummies . Getting started with geometry basics. Introducing geometry ; Building your geometric foundation ; Sizing up segments and analyzing angles Introducing proofs. Prelude to proofs ; Your starter kit of easy theorems and short proofs ; The ultimate guide to tackling a longer proof Triangles: polygons of the three-sided variety. Grasping triangle fundamentals ; Regarding right triangles ; Completing congruent triangle proofs Polygons of the four-or-more-sided variety. The seven wonders of the quadrilateral world ; Proving that you have a particular quadrilateral ; Polygon formulas: area, angles, and diagonals ; Similarity: same shape, different size Working with not-so-vicious circles. Coming around to circle basics ; Circle formulas and theorems Going deep with 3-D geometry. 3-D space: proofs in a higher plane of existence ; Getting a grip on solid geometry Placement, points, and pictures: alternative geometry topics. Coordinate geometry ; Changing the scene with geometric transformations ; Locating loci and constructing constructions The part of tens. Ten things to use as reasons in geometry proofs ; Ten cool geometry problems. Does the thought of geometry make you jittery? You're not alone. Fortunately, this down-to-earth guide helps you approach it from a new angle, making it easier than ever to conquer your fears and score your highest in geometry. From getting started with geometry basics to making friends with lines and angles, you'll be proving triangles congruent, calculating circumference, using formulas, and serving up pi in no time. Geometry is a subject full of mathematical richness and beauty. But it's a subject that bewilders many students because it's so unlike the math they've done before{u2014}it requires the use of deductive logic in formal proofs. If you're having a hard time wrapping your mind around what that even means, you've come to the right place! Inside, you'll find out how a proof's chain of logic works and even discover some secrets for getting past rough spots along the way. You don't have to be a math genius to grasp geometry, and this book helps you get un-stumped in a hurry! Students studying geometry in school will certainly learn about lines and angles, circles and triangles, and they'll find everything they need to master those topics. But Geometry is so much more than shapes! Proofs are at the heart of any Geometry course, and they're most often where students struggle. Geometry For Dummies, 3rd Edition, is overflowing with helpful and practical, plain-English information about proofs to help students succeed. --Publisher's description.