
Geometry Essentials For Dummies
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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
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Content
- Intro
- Title Page
- Copyright Page
- Table of Contents
- 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
- One-dimensional shapes
- Two-dimensional shapes
- Three-dimensional shapes
- Geometry Proofs
- Am I Ever Going to Use This?
- When you'll use your knowledge of shapes
- When you'll use your knowledge of proofs
- Getting Down with Definitions
- A Few Points on Points
- Lines, Segments, and Rays
- Horizontal and vertical lines
- Doubling up with pairs of lines
- Investigating the Plane Facts
- Everybody's Got an Angle
- Five types of angles
- Angle pairs
- Bisection and Trisection
- Segments
- Angles
- Chapter 2 Geometry Proof Starter Kit
- The Lay of the (Proof) Land
- Reasoning with If-Then Logic
- If-then chains of logic
- Definitions, theorems, and postulates
- Bubble logic
- Complementary and Supplementary Angles
- Addition and Subtraction
- Addition theorems
- Subtraction theorems
- 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
- Scalene triangles
- Isosceles triangles
- Equilateral triangles
- Triangle Classification by Angles
- The Triangle Inequality Principle
- Sizing up Triangle Area
- A triangle's altitude or height
- Determining a triangle's area
- Regarding Right Triangles
- The Pythagorean Theorem
- Pythagorean Triple Triangles
- The Fab Four triangles
- Families of Pythagorean triple triangles
- Two Special Right Triangles
- The 45degree-45degree-90degree triangle
- The 30degree-60degree-90degree triangle
- Chapter 5 Congruent Triangle Proofs
- Proving Triangles Congruent
- SSS: The side-side-side method
- SAS: Side-angle-side
- ASA: The angle-side-angle tack
- AAS: Angle-angle-side
- Last but not least: HLR
- Taking the Next Step with CPCTC
- Defining CPCTC
- Tackling a CPCTC proof
- The Isosceles Triangle Theorems
- The Two Equidistance Theorems
- Determining a perpendicular bisector
- Using a perpendicular bisector
- Chapter 6 Quadrilaterals
- Parallel Line Properties
- Parallel lines with a transversal
- The transversal theorems
- The Seven Special Quadrilaterals
- Working with Auxiliary Lines
- The Properties of Quadrilaterals
- Properties of the parallelogram
- Properties of the three special parallelograms
- Properties of the kite
- Properties of the trapezoid and the isosceles trapezoid
- Proving That You've Got a Particular Quadrilateral
- Proving you've got a parallelogram
- Proving that you've got a rectangle, rhombus, or square
- Proving that you've got a kite
- Chapter 7 Polygon Formulas
- The Area of Quadrilaterals
- Quadrilateral area formulas
- Why the formulas work
- Trying a few area problems
- The Area of Regular Polygons
- The polygon area formulas
- Tackling an area problem
- Angle and Diagonal Formulas
- Interior and exterior angles
- A polygon angle problem
- Criss-crossing with diagonals
- Chapter 8 Similarity
- Similar Figures
- Defining similar polygons
- How similar figures line up
- Solving a similarity problem
- Proving Triangles Similar
- Tackling an AA proof
- Using SSS~
- An SAS~ proof
- Splitting Right Triangles with the Altitude-on-Hypotenuse Theorem
- More Proportionality Theorems
- The Side-Splitter Theorem
- The Angle-Bisector Theorem
- Chapter 9 Circle Basics
- Radii, Chords, and Diameters
- Five circle theorems
- Using extra radii
- Arcs and Central Angles
- Tangents
- The Pizza Slice Formulas
- Determining arc length
- Sector and segment area
- The Angle-Arc Formulas
- Angles on a circle
- Angles inside a circle
- Angles outside a circle
- Keeping the formulas straight
- The Power Theorems
- The Chord-Chord Theorem
- The Tangent-Secant Theorem
- The Secant-Secant Theorem
- Condensing the power theorems into a single idea
- Chapter 10 3-D Geometry
- Flat-Top Figures
- Pointy-Top Figures
- Spheres
- Chapter 11 Coordinate Geometry
- The Coordinate Plane
- Slope, Distance, and Midpoint
- The slope dope
- The distance formula
- The midpoint formula
- Trying out the formulas
- Equations for Lines and Circles
- Line equations
- The circle equation
- 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
- EULA
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