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End User License Agreement
by Mark Ryan
Geometry Essentials For Dummies
Cover
Introduction
About This Book
Conventions Used in This Book
Foolish Assumptions
Icons Used in This Book
Where to Go from Here
Chapter 1: An Overview of Geometry
The Geometry of Shapes
Geometry Proofs
Am I Ever Going to Use This?
Getting Down with Definitions
A Few Points on Points
Lines, Segments, and Rays
Investigating the Plane Facts
Everybody’s Got an Angle
Bisection and Trisection
Chapter 2: Geometry Proof Starter Kit
The Lay of the (Proof) Land
Reasoning with If-Then Logic
Complementary and Supplementary Angles
Addition and Subtraction
Like Multiples and Like Divisions
Congruent Vertical Angles
Transitivity and Substitution
Chapter 3: Tackling a Longer Proof
Making a Game Plan
Using All the Givens
Using If-Then Logic
Chipping Away at the Problem
Working Backward
Filling in the Gaps
Writing out the Finished Proof
Chapter 4: Triangle Fundamentals
Taking in a Triangle’s Sides
Triangle Classification by Angles
The Triangle Inequality Principle
Sizing up Triangle Area
Regarding Right Triangles
The Pythagorean Theorem
Pythagorean Triple Triangles
Two Special Right Triangles
Chapter 5: Congruent Triangle Proofs
Proving Triangles Congruent
Taking the Next Step with CPCTC
The Isosceles Triangle Theorems
The Two Equidistance Theorems
Chapter 6: Quadrilaterals
Parallel Line Properties
The Seven Special Quadrilaterals
Working with Auxiliary Lines
The Properties of Quadrilaterals
Proving That You’ve Got a Particular Quadrilateral
Chapter 7: Polygon Formulas
The Area of Quadrilaterals
The Area of Regular Polygons
Angle and Diagonal Formulas
Chapter 8: Similarity
Similar Figures
Proving Triangles Similar
Splitting Right Triangles with the Altitude-on-Hypotenuse Theorem
More Proportionality Theorems
Chapter 9: Circle Basics
Radii, Chords, and Diameters
Arcs and Central Angles
Tangents
The Pizza Slice Formulas
The Angle-Arc Formulas
The Power Theorems
Chapter 10: 3-D Geometry
Flat-Top Figures
Pointy-Top Figures
Spheres
Chapter 11: Coordinate Geometry
The Coordinate Plane
Slope, Distance, and Midpoint
Equations for Lines and Circles
Chapter 12: Ten Big Reasons to Use in Proofs
The Reflexive Property
Vertical Angles Are Congruent
The Parallel-Line Theorems
Two Points Determine a Line
All Radii Are Congruent
If Sides, Then Angles
If Angles, Then Sides
Triangle Congruence
CPCTC
Triangle Similarity
Index
About the Author
Connect with Dummies
End User License Agreement
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