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# Geometry Study Guide

## Overview

"Boost Your grades with this illustrated Study Guide. You will use it from college to graduate school and beyond.

FEATURES:
- Clear and concise explanations
- Difficult concepts are explained in simple terms
- Illustrated with graphs and diagrams

Geometry Background

Euclidean Geometry
Euclidean Space
Line
Line Segment
Incidence of planes and lines

Incidence Structure

Euclidean Distance

One-dimensional distance
Two-dimensional distance
Three-dimensional distance

Postulate
The Plane Areas of Mathematics
Translation
Translational Symmetry
Similarity

Triangles

Triangle

Types of triangles
Points, lines and circles associated with a triangle
Computing the area of a triangle
Using vectors
Using trigonometry
Using coordinates
Using Heron's formula
Ceva's Theorem
Heron's Formula

Equilateral Triangle
Right Angle
Pythagorean Theorem
Pythagorean Triple
Heronian Triangle
Triangle Inequality
Pedoe's Inequality
Similar triangles

Parallel Lines

Congruence
Parallel Postulate

Polygons

Convex polygon
Internal Angle
Diagonal
Perimeter

Isosceles Trapezoid
Parallelogram
Kite
Rhombus, Rhomboid
Rectangle
Square

Star Polygon

Circles

Analytic results
Properties
Calculating the parameters
Area of a Disk
Circular Sector
Circular Segment
Circumference
Nine-point Circle

Transformational Geometry

Scaling
Rotation,

Euler's Formula,
Rotation Matrix,
Quaternions and Spatial Rotation

Reflection

Coordinate Rotations and Reflections

Linear Map

Solid Geometry

Dihedral angle and Solid angle
The Cube

Cuboid
Hypercube Graph
Parallelepiped

Prisms
The Tetrahedron and Pyramid
Octahedron, Dodecahedron, Icosahedron
Cones and Cylinders
The Sphere and Spheroid,

Ellipsoid
Paraboloid
Hyperboloid "

## Author Information

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## Product Details

Mobile Reference

• ### Publish Date

January 21, 2010

• ### eBook ISBN

9781605010922

3.10 MB

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