Geometry Study Guide

Boost Your grades with this illustrated study guide. You will use it from college to graduate school and beyond. FREE Geometry Background and Triangles chapters in the trial version.

Features

Clear and concise explanations
Difficult concepts are explained in simple terms
Illustrated with graphs and diagrams
Table of Contents

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
Quadrilateral
Isosceles Trapezoid
Parallelogram
Kite
Rhombus, Rhomboid
Rectangle
Square
Cyclic Quadrilateral, Brahmagupta's formula
Tangential Quadrilateral
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,
Quadrics:
Ellipsoid
Paraboloid
Hyperboloid