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