Introduction 1 About This Book 1 Conventions Used in This Book 2 Foolish Assumptions 2 Icons Used in This Book 3 Where to Go from Here 3 Chapter 1: An Overview of Geometry 5 The Geometry of Shapes 6 One-dimensional shapes 6 Two-dimensional shapes 6 Three-dimensional shapes 6 Geometry Proofs 6 Am I Ever Going to Use This? 7 When you''ll use your knowledge of shapes 7 When you''ll use your knowledge of proofs 8 Getting Down with Definitions 9 A Few Points on Points 11 Lines, Segments, and Rays 12 Horizontal and vertical lines 12 Doubling up with pairs of lines 13 Investigating the Plane Facts 14 Everybody''s Got an Angle 14 Five types of angles 15 Angle pairs 16 Bisection and Trisection 18 Segments 18 Angles 18 Chapter 2: Geometry Proof Starter Kit 21 The Lay of the (Proof) Land 21 Reasoning with If-Then Logic 23 If-then chains of logic 24 Definitions, theorems, and postulates 25 Bubble logic 26 Complementary and Supplementary Angles 27 Addition and Subtraction 29 Addition theorems 29 Subtraction theorems 33 Like Multiples and Like Divisions 34 Congruent Vertical Angles 36 Transitivity and Substitution 37 Chapter 3: Tackling a Longer Proof 41 Making a Game Plan 42 Using All the Givens 42 Using If-Then Logic 43 Chipping Away at the Problem 45 Working Backward 47 Filling in the Gaps 49 Writing out the Finished Proof 49 Chapter 4: Triangle Fundamentals 51 Taking in a Triangle''s Sides 51 Scalene triangles 52 Isosceles triangles 52 Equilateral triangles 52 Triangle Classification by Angles 52 The Triangle Inequality Principle 53 Sizing up Triangle Area 54 A triangle''s altitude or height 54 Determining a triangle''s area 56 Regarding Right Triangles 57 The Pythagorean Theorem 58 Pythagorean Triple Triangles 60 The Fab Four triangles 61 Families of Pythagorean triple triangles 61 Two Special Right Triangles 64 The 45 - 45 - 90 triangle 64 The 30 - 60 - 90 triangle 66 Chapter 5: Congruent Triangle Proofs 69 Proving Triangles Congruent 69 SSS: The side-side-side method 70 SAS: Side-angle-side 72 ASA: The angle-side-angle tack 74 AAS: Angle-angle-side 74 Last but not least: HLR 75 Taking the Next Step with CPCTC 75 Defining CPCTC 76 Tackling a CPCTC proof 76 The Isosceles Triangle Theorems 79 The Two Equidistance Theorems 81 Determining a perpendicular bisector 81 Using a perpendicular bisector 83 Chapter 6: Quadrilaterals 85 Parallel Line Properties 85 Parallel lines with a transversal 85 The transversal theorems 87 The Seven Special Quadrilaterals 89 Working with Auxiliary Lines 90 The Properties of Quadrilaterals 93 Properties of the parallelogram 93 Properties of the three special parallelograms 95 Properties of the kite 98 Properties of the trapezoid and the isosceles trapezoid 99 Proving That You''ve Got a Particular Quadrilateral 100 Proving you''ve got a parallelogram 100 Proving that you''ve got a rectangle, rhombus, or square 103 Proving that you''ve got a kite 104 Chapter 7: Polygon Formulas 107 The Area of Quadrilaterals 107 Quadrilateral area formulas 108 Why the formulas work 108 Trying a few area problems 110 The Area of Regular Polygons 113 The polygon area formulas 114 Tackling an area problem 114 Angle and Diagonal Formulas 115 Interior and exterior angles 116 A polygon angle problem 117 Criss-crossing with diagonals 118 Chapter 8: Similarity 119 Similar Figures 119 Defining similar polygons 119 How similar figures line up 121 Solving a similarity problem 122 Proving Triangles Similar 124 Tackling an AA proof 125 Using SSS~ 126 An SAS~ proof 127 Splitting Right Triangles with the Altitude-on-Hypotenuse Theorem 128 More Proportionality Theorems 130 The Side-Splitter Theorem 130 The Angle-Bisector Theorem 132 Chapter 9: Circle Basics 135 Radii, Chords, and Diameters 135 Five circle theorems 136 Using extra radii 136 Arcs and Central Angles 138 Tangents 138 The Pizza Slice Formulas 140 Determining arc length 140 Sector and segment area 141 The Angle-Arc Formulas 143 Angles on a circle 144 Angles inside a circle 144 Angles outside a circle 145 Keeping the formulas straight 146 The Power Theorems 147 The Chord-Chord Theorem 148 The Tangent-Secant Theorem 149 The Secant-Secant Theorem 149 Condensing the power theorems into a single idea 150 Chapter 10: 3-D Geometry 151 Flat-Top Figures 151 Pointy-Top Figures 154 Spheres 159 Chapter 11: Coordinate Geometry 161 The Coordinate Plane 161 Slope, Distance, and Midpoint 162 The slope dope 162 The distance formula 164 The midpoint formula 165 Trying out the formulas 166 Equations for Lines and Circles 167 Line equations 168 The circle equation 168 Chapter 12: Ten Big Reasons to Use in Proofs 171 The Reflexive Property 171 Vertical Angles are Congruent 171 The Parallel-Line Theorems 172 Two Points Determine a Line 172 All Radii are Congruent 173 If Sides, Then Angles 173 If Angles, Then Sides 173 Triangle Congruence 173 CPCTC 174 Triangle Similarity 174 Index 175.