Geometry Study Guide

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


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