Polygons
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A polygon is a closed figure that is the union of line segments in a plane.  A polygon has three or more sides.
A polygon has the same number of angles as sides.

Polygons can be classified as either convex or concave.
 

  A polygon is convex if no line that contains a side of the polygon contains a point in the interior of the polygon.  In a convex polygon, each interior angle measures less than 180 degrees. 
Concave polygons "cave-in" to their interiors, creating at least one interior angle greater than 180 degrees (a reflex angle). 

Unless otherwise stated, we will be discussing convex polygons.

 

Types of Polygons

Listed below are some of the more commonly used polygons.
(Do not assume that the diagrams under the "Graphic" column are "regular" polygons.  Do not assume any specific details about the diagrams such as the length of the sides or measures of the angles.)

Polygon Graphic Sides Angles Vertices Diagonals Number
Triangles
Triangle 3 3 3 0 1
Quadrilateral 4 4 4 2 2
Pentagon 5 5 5 5 3
Hexagon 6 6 6 9 4
Heptagon or Septagon 7 7 7 14 5
Octagon 8 8 8 20 6
Nonagon or Novagon 9 9 9 27 7
Decagon 10 10 10 35 8
Dodecagon 12 12 12 54 10
n-gon --- n n n (n - 2)

 

A polygon is equilateral if all of its sides are of the same length.
A polygon is equiangular if all of its angles are of equal measure.

A regular polygon is a polygon that is both equilateral and equiangular.