Details

Geometry Essentials For Dummies


Geometry Essentials For Dummies


1. Aufl.

von: Mark Ryan

8,99 €

Verlag: Wiley
Format: PDF
Veröffentl.: 16.04.2019
ISBN/EAN: 9781119590477
Sprache: englisch
Anzahl Seiten: 192

DRM-geschütztes eBook, Sie benötigen z.B. Adobe Digital Editions und eine Adobe ID zum Lesen.

Beschreibungen

<p><i>Geometry Essentials For Dummies</i> (9781119590446) was previously published as <i>Geometry Essentials For Dummies </i>(9781118068755). While this version features a new <i>Dummies</i> cover and design, the content is the same as the prior release and should not be considered a new or updated product.</p> <p> </p> <p><b>Just the critical concepts you need to score high in geometry</b></p> <p>This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams.</p> <ul> <li>Get down to the basics — get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals</li> <li>Conquer proofs with confidence — follow easy-to-grasp instructions for understanding the components of a formal geometry proof</li> <li>Take triangles in strides — learn how to take in a triangle's sides, analyze its angles, work through an SAS proof, and apply the Pythagorean Theorem</li> <li>Polish up on polygons — get the lowdown on quadrilaterals and other polygons: their angles, areas, properties, perimeters, and much more</li> </ul>
<p><b>Introduction 1</b></p> <p>About This Book 1</p> <p>Conventions Used in This Book 2</p> <p>Foolish Assumptions 2</p> <p>Icons Used in This Book 3</p> <p>Where to Go from Here 3</p> <p><b>Chapter 1: An Overview of Geometry</b><b> 5</b></p> <p>The Geometry of Shapes 6</p> <p>One-dimensional shapes 6</p> <p>Two-dimensional shapes 6</p> <p>Three-dimensional shapes 6</p> <p>Geometry Proofs 6</p> <p>Am I Ever Going to Use This? 7</p> <p>When you’ll use your knowledge of shapes 7</p> <p>When you’ll use your knowledge of proofs 8</p> <p>Getting Down with Definitions 9</p> <p>A Few Points on Points 11</p> <p>Lines, Segments, and Rays 12</p> <p>Horizontal and vertical lines 12</p> <p>Doubling up with pairs of lines 13</p> <p>Investigating the Plane Facts 14</p> <p>Everybody’s Got an Angle 14</p> <p>Five types of angles 15</p> <p>Angle pairs 16</p> <p>Bisection and Trisection 18</p> <p>Segments 18</p> <p>Angles 18</p> <p><b>Chapter 2: Geometry Proof Starter Kit</b><b> 21</b></p> <p>The Lay of the (Proof) Land 21</p> <p>Reasoning with If-Then Logic 23</p> <p>If-then chains of logic 24</p> <p>Definitions, theorems, and postulates 25</p> <p>Bubble logic 26</p> <p>Complementary and Supplementary Angles 27</p> <p>Addition and Subtraction 29</p> <p>Addition theorems 29</p> <p>Subtraction theorems 33</p> <p>Like Multiples and Like Divisions 34</p> <p>Congruent Vertical Angles 36</p> <p>Transitivity and Substitution 37</p> <p><b>Chapter 3: Tackling a Longer Proof</b><b> 41</b></p> <p>Making a Game Plan 42</p> <p>Using All the Givens 42</p> <p>Using If-Then Logic 43</p> <p>Chipping Away at the Problem 45</p> <p>Working Backward 47</p> <p>Filling in the Gaps 49</p> <p>Writing out the Finished Proof 49</p> <p><b>Chapter 4: Triangle Fundamentals</b><b> 51</b></p> <p>Taking in a Triangle’s Sides 51</p> <p>Scalene triangles 52</p> <p>Isosceles triangles 52</p> <p>Equilateral triangles 52</p> <p>Triangle Classification by Angles 52</p> <p>The Triangle Inequality Principle 53</p> <p>Sizing up Triangle Area 54</p> <p>A triangle’s altitude or height 54</p> <p>Determining a triangle’s area 56</p> <p>Regarding Right Triangles 57</p> <p>The Pythagorean Theorem 58</p> <p>Pythagorean Triple Triangles 60</p> <p>The Fab Four triangles 61</p> <p>Families of Pythagorean triple triangles 61</p> <p>Two Special Right Triangles 64</p> <p>The 45 - 45 - 90 triangle 64</p> <p>The 30 - 60 - 90 triangle 66</p> <p><b>Chapter 5: Congruent Triangle Proofs</b><b> 69</b></p> <p>Proving Triangles Congruent 69</p> <p>SSS: The side-side-side method 70</p> <p>SAS: Side-angle-side 72</p> <p>ASA: The angle-side-angle tack 74</p> <p>AAS: Angle-angle-side 74</p> <p>Last but not least: HLR 75</p> <p>Taking the Next Step with CPCTC 75</p> <p>Defining CPCTC 76</p> <p>Tackling a CPCTC proof 76</p> <p>The Isosceles Triangle Theorems 79</p> <p>The Two Equidistance Theorems 81</p> <p>Determining a perpendicular bisector 81</p> <p>Using a perpendicular bisector 83</p> <p><b>Chapter 6: Quadrilaterals</b><b> 85</b></p> <p>Parallel Line Properties 85</p> <p>Parallel lines with a transversal 85</p> <p>The transversal theorems 87</p> <p>The Seven Special Quadrilaterals 89</p> <p>Working with Auxiliary Lines 90</p> <p>The Properties of Quadrilaterals 93</p> <p>Properties of the parallelogram 93</p> <p>Properties of the three special parallelograms 95</p> <p>Properties of the kite 98</p> <p>Properties of the trapezoid and the isosceles trapezoid 99</p> <p>Proving That You’ve Got a Particular Quadrilateral 100</p> <p>Proving you’ve got a parallelogram 100</p> <p>Proving that you’ve got a rectangle, rhombus, or square 103</p> <p>Proving that you’ve got a kite 104</p> <p><b>Chapter 7: Polygon Formulas</b><b> 107</b></p> <p>The Area of Quadrilaterals 107</p> <p>Quadrilateral area formulas 108</p> <p>Why the formulas work 108</p> <p>Trying a few area problems 110</p> <p>The Area of Regular Polygons 113</p> <p>The polygon area formulas 114</p> <p>Tackling an area problem 114</p> <p>Angle and Diagonal Formulas 115</p> <p>Interior and exterior angles 116</p> <p>A polygon angle problem 117</p> <p>Criss-crossing with diagonals 118</p> <p><b>Chapter 8: Similarity</b><b> 119</b></p> <p>Similar Figures 119</p> <p>Defining similar polygons 119</p> <p>How similar figures line up 121</p> <p>Solving a similarity problem 122</p> <p>Proving Triangles Similar 124</p> <p>Tackling an AA proof 125</p> <p>Using SSS~ 126</p> <p>An SAS~ proof 127</p> <p>Splitting Right Triangles with the Altitude-on-Hypotenuse Theorem 128</p> <p>More Proportionality Theorems 130</p> <p>The Side-Splitter Theorem 130</p> <p>The Angle-Bisector Theorem 132</p> <p><b>Chapter 9: Circle Basics</b><b> 135</b></p> <p>Radii, Chords, and Diameters 135</p> <p>Five circle theorems 136</p> <p>Using extra radii 136</p> <p>Arcs and Central Angles 138</p> <p>Tangents 138</p> <p>The Pizza Slice Formulas 140</p> <p>Determining arc length 140</p> <p>Sector and segment area 141</p> <p>The Angle-Arc Formulas 143</p> <p>Angles on a circle 144</p> <p>Angles inside a circle 144</p> <p>Angles outside a circle 145</p> <p>Keeping the formulas straight 146</p> <p>The Power Theorems 147</p> <p>The Chord-Chord Theorem 148</p> <p>The Tangent-Secant Theorem 149</p> <p>The Secant-Secant Theorem 149</p> <p>Condensing the power theorems into a single idea 150</p> <p><b>Chapter 10: 3-D Geometry</b><b> 151</b></p> <p>Flat-Top Figures 151</p> <p>Pointy-Top Figures 154</p> <p>Spheres 159</p> <p><b>Chapter 11: Coordinate Geometry</b><b> 161</b></p> <p>The Coordinate Plane 161</p> <p>Slope, Distance, and Midpoint 162</p> <p>The slope dope 162</p> <p>The distance formula 164</p> <p>The midpoint formula 165</p> <p>Trying out the formulas 166</p> <p>Equations for Lines and Circles 167</p> <p>Line equations 168</p> <p>The circle equation 168</p> <p><b>Chapter 12: Ten Big Reasons to Use in Proofs</b><b> 171</b></p> <p>The Reflexive Property 171</p> <p>Vertical Angles are Congruent 171</p> <p>The Parallel-Line Theorems 172</p> <p>Two Points Determine a Line 172</p> <p>All Radii are Congruent 173</p> <p>If Sides, Then Angles 173</p> <p>If Angles, Then Sides 173</p> <p>Triangle Congruence 173</p> <p>CPCTC 174</p> <p>Triangle Similarity 174</p> <p>Index 175</p>
<p><b>Mark Ryan</b> is the owner of The Math Center in the Chicago area, where he teaches students in all levels of mathematics, from pre-algebra to calculus. He is the author of <i>Calculus For Dummies and Geometry For Dummies.</i>
<ul> <li>Critical theorems for geometry proofs</li> <li>The principles and formulas you need to know</li> <li>Key concepts in quick, focused lessons</li> </ul> <p><b>All you need to get in shape for geometry</b> <p>This practical, friendly guide focuses on critical concepts taught in a typical geometry course. Get a handle on the basics — from lines, segments, and angles to vertices, altitudes, and diagonals. Learn the properties of triangles, parallelograms, circles, and cylinders. Master the skills and strategies you need to write geometry proofs. <i>Geometry Essentials For Dummies</i> is perfect for cramming, doing homework, or as a reference for parents helping kids study for exams. <p><b>Inside...</b> <ul> <li>Common geometry terms</li> <li>Tips for tackling geometry proofs</li> <li>The quadrilateral family</li> <li>Straight talk on circles</li> <li>Essential triangle formulas</li> <li>Spheres, cylinders, prisms, and pyramids</li> </ul>

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