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A polygon is a 2-dimensional closed figure that is the union of line segments in a plane. A polygon has three or more sides.

You already have a good understanding of 3-sided and 4-sided polygons from your previous studies of geometry.

3-sided polygons - triangles - all types
(acute, right, obtuse, equiangular, scalene, isosceles, equilateral)

4-sided polygons - quadrilaterals - all types
(kite, rhombus, square, trapezoid, parallelogram, rectangle)

We will now enhance these previous concepts
by adding more "sides" to the figures,
as well as adding some new information.
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Classifications of Polygons

 

bullet Polygons can be classified as either regular or irregular (meaning not regular).

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A regular polygon is a polygon in which all of the sides are of equal length and all of the angles are of equal measure.
It is both equilateral and equiangular.

You have already been working with some regular polygons.
A regular triangle is an equilateral
triangle (also called an equiangular triangle).
ptriangle
All of its sides are the same length.
All of its angles are the same measure (60º).
A regular quadrilateral is a square.
redsquare
All of its sides are the same length.
All of its angles are the same measure (90º).

In a regular polygon, all of its interior angles are of the same measure and all of its sides are the same length.
regularpoly
Regular Hexagon
In an irregular polygon, the interior angles may be of different measures and the sides may be different lengths.
irregular poly
Irregular Hexagon

beware
The term "polygon" refers to a type of figure which may be regular or irregular. Do NOT assume "polygon" means "regular polygon". If a polygon is a regular polygon, it will be stated as such.
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Parts of Regular Polygons



Regular Pentagon

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The center, (O), of a regular polygon, is a point in the interior of the polygon equidistant from each vertex. It is also the center of the inscribed and circumscribed circles. The radius is the distance from the center to any vertex.
The central angle of a regular polygon is formed by connecting the center to two adjacent vertices. All central angles are of equal measure in a regular polygon.
Irregular polygons are not described as having a "center" which is equidistant from each vertex. As such, an irregular polygon does not have central angles or radii. An irregular polygon does, however, have a center of gravity or a centroid.

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Types of Polygons

 


The table below shows some of the more commonly used polygons.
Do NOT assume that the diagrams in the "Figure" column are "regular" polygons.
Polygon
Figure
Sides
Angles
Diagonals
# of Triangles
from 1 vertex
Triangle
ptriangle
3
3
0
1
 ptriangle
Quadrilateral
pquada
4
4
2
2
 ptriangle
Pentagon
ppent
5
5
5
3
 ptriangle
Hexagon
phex
6
6
9
4
 ptriangle
Heptagon or Septagon
phe
7
7
14
5
 ptriangle
Octagon
phepta
8
8
20
6
 ptriangle
Nonagon or Novagon
poct
9
9
27
7
 ptriangle
Decagon
pdec
10
10
35
8
 ptriangle
Dodecagon
pdd
12
12
54
10
 ptriangle

 

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