Geometry Essentials for Dummies PDF
Preview Geometry Essentials for Dummies
® Geometry Essentials For Dummies Visit www.dummies.com/cheatsheet/geometryessentials to view this book's cheat sheet. 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 45°- 45°- 90° triangle The 30°- 60°- 90° 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 Cheat Sheet
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