Geometry essentials for dummies - Ryan, Mark, 1955- (Hoboken, NJ : Wiley Pub., 2011)
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.
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.
Includes index.
Keywords: Geometry