Geometry Essentials For Dummies

Mark Ryan

eBook (pdf), 192 Nombre de pages

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Geometry Essentials For Dummies (9781119590446) was previously published as Geometry Essentials For Dummies (9781118068755). Whil...

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Description

Geometry Essentials For Dummies (9781119590446) was previously published as Geometry Essentials For Dummies (9781118068755). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Just the critical concepts you need to score high in geometry 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. Get down to the basics -- get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conquer proofs with confidence -- follow easy-to-grasp instructions for understanding the components of a formal geometry proof 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 Polish up on polygons -- get the lowdown on quadrilaterals and other polygons: their angles, areas, properties, perimeters, and much more
Auteur
Mark Ryan 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 Calculus For Dummies and Geometry For Dummies.
Texte du rabat
* Critical theorems for geometry proofs * The principles and formulas you need to know Key concepts in quick, focused lessons *All you need to get in shape for geometry 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. Geometry Essentials For Dummies is perfect for cramming, doing homework, or as a reference for parents helping kids study for exams. Inside... * Common geometry terms * Tips for tackling geometry proofs * The quadrilateral family * Straight talk on circles * Essential triangle formulas * Spheres, cylinders, prisms, and pyramids
Résumé
Geometry Essentials For Dummies (9781119590446) was previously published as Geometry Essentials For Dummies (9781118068755). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Just the critical concepts you need to score high in geometry 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. * Get down to the basics get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals * Conquer proofs with confidence follow easy-to-grasp instructions for understanding the components of a formal geometry proof * 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 * Polish up on polygons get the lowdown on quadrilaterals and other polygons: their angles, areas, properties, perimeters, and much more
Contenu
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 ...