Question

What is the difference between an equiangular polygon, equilateral polygon and a regular polygon? Provide an example of each.

Answer 1

Hint: We have to know that a polygon is formed when the starting point and ending point is the same or we can say that it is a closed figure. We will first define equiangular, equilateral and regular polygons by recollecting the concepts and then after that we will be able to provide examples of each one.

Complete step by step answer:
Equilateral polygons are polygons whose sides are congruent or of the same size. An example of an Equilateral polygon would be a rhombus. A rhombus has all four sides of the same size. Also, a rhombus does not have all angles equal. In a rhombus, we have opposite sides which are parallel to each other. In the below figure, side AC is parallel to BD and side AB is parallel to CD.

Equiangular polygons are polygons whose all angles are equal. An example of an equiangular polygon would be a rectangle. A rectangle has all four angles equal, each being \[{{90}^{\circ }}\]. In a rectangle side AB and side CD are of equal length and parallel to each other. Similarly, side AC and side BD are of equal length and parallel to each other. The diagonals are also perpendicular to each other.

A polygon which can be classified as both an equilateral and an equiangular polygon is a regular polygon. An example of a regular polygon is a square. The sides of a regular polygon would be equidistant from a point within the polygon which is the centre of the polygon. In the figure given below, square ABCD, all 4 sides are of equal length and the diagonals are equal and perpendicular to each other.

Note: Do not confuse between equiangular, equilateral and regular polygons. A simple way to remember them is to break the names down into simple parts like – “equi-angular” which means angles are equal, “equi-lateral” which means lateral sides are equal. A combination of these two make a regular polygon.