A polygon means a two dimensional shape that encloses a surface with a number of line segments called sides.
In algebra how do we classify the expressions? If it is single term we call it a monomial. Same way we use the terms binomial for two terms and trinomial for three terms. For expressions of higher terms we use a common nomenclature as polynomials.
Similarly in geometry two dimensional shapes are classified as triangles ( 3sides), quadrilaterals ( sides), pentagons ( 5 sides), hexagons( 6 sides), heptagon (7 sides), octagons (8 sides), nonagons (9 sides) and decagons ( 10 sides). For shapes with higher number of sides we refer them as polygons.
The names heptagons, nonagons and decagons are not very familiar and hence they are also referred as polygons.
Types of Polygons
If all the sides of a polygon are congruent, then the polygon is called as a regular polygon. If the sides are not congruent (even if one side is different) then the polygon is a irregular polygon.
An example of an octagon when it is regular and when it is irregular is shown below.
Polygons – Basic Parameters
Consider the quadrilateral shown below, as an example of a polygon.
Sides
As defined earlier a polygon encloses a surface with a number of line segments called sides.
The sides of the above polygon are AB, BC, CD and DA.
Vertices
The points of intersections of the sides are defined as the vertices of the polygons.
The vertices of the above polygon are A, B, C and D.
Angles
The rotational displacement between the sides are called the angles of the polygons.
The angle between the sides interior of the polygon are called interior angles and generally noted by the names of the vertices. The angle between the sides exterior of the polygon are called exterior angles of the polygons.
In the above polygon, at vertex A, the angle DAB (that is angle A) is interior angle and angle DAX is the exterior angle.
As you see in the above diagram, at any vertex, the interior angle and the exterior angles are supplementary.
Diagonals
The line segments connecting two vertices not adjacent to each other are called the diagonals of the polygons.
In the above polygon the diagonals are AC and BD.
Polygons and Circles
There is a constant debate on this subject.
It is true that as the number of sides of a polygon are very large, the vertices become very close to each other. Hence some mathematician argue that a circle could be described as a regular polygon with number of sides as infinity.
But in mathematics infinity is neither a defined number nor a real number. Hence the concept of infinite number of sides is not acceptable. Therefore, a circle can not be considered as a polygon.
Related Tags
Types of Polygons, Basic parameters of Polygons, Study of Polygons