Geometry Essentials for Dummies

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 Open the book and find: Plain-English explanations of geometry terms Tips for tackling geometry proofs The seven members of the quadrilateral family Straight talk on circles Essential triangle formulas The lowdown on 3-D: spheres, cylinders, prisms, and pyramids Ten things to use as reasons in geometry proofs Learn to: Core concepts about the geometry of shapes and geometry proofs Critical theorems, postulates, and definitions The principles and formulas you need to know An overview of geometry. The geometry of shapes ; Geometry proofs ; Am I ever going to use this? ; Getting down with definitions ; Lines, segments, and rays ; Investigating the plane facts ; Everybody's got an angle ; Bisection and trisection Geometry proof starter kit. The lay of the (proof) land ; Reasoning with If-Then logic ; Complementary and supplementary angles ; Addition and subtractions ; Like multiples and like divisions ; Congruent vertical angles ; Transitivity and substitution 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 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 Congruent triangle proofs. Proving triangles congruent ; Taking the next step with CPCTC ; The Isosceles Triangle Theorems ; The two equidistance theorems Quadrilaterals. Parallel line properties ; The seven special quadrilaterals ; Working with auxiliary lines ; The properties of quadrilaterals ; Proving that you've got a particular quadrilateral Polygon formulas. The areas of quadrilaterals ; The area of regular polygons ; Angle and diagonal formulas Similarity. Similar figures ; Proving triangles similar ; Splitting right triangles with the Altitude-on-Hypotenuse Theorem ; More proportionality theorems Circle basics. Radii, chords, and diameters ; Arcs and central angles ; Tangents ; The pizza slice formulas ; The angle-arc formulas ; The power theorems 3-D geometry. Flat-top figures ; Pointy-top figures ; Spheres Coordinate geometry. The coordinate plane ; Slope, distance, and midpoint ; Equations for lines and circles 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. A practical guide to the critical concepts taught in a typical geometry course. Provides the basics you need to score high in geometry, or for parents helping kids study for exams.