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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
Autorentext
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.
Klappentext
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...
Zusammenfassung
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.
Inhalt
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 ...