# Quadrilaterals

## Introduction

**Polygon:** Polygon is a combination of two Greek words Polus + Gonia, in which Polus means many and Gonia means Corner or angle. Thus, a plane figure bounded by a finite straight line segment in loop to form a closed chain is called a polygon.

## Classification of Polygons

Polygons are classified as per their sides or vertices they have.

**(a) Triangle:** A triangle has three sides and three vertices.

**(b) Quardilateral:** A quardilateral has four sides and four vertices.

**(c) Pentagon:** (Penta means five) A pentagon has five sides and five vertices.

**(d) Hexagon:** (Hexa means six) A hexagon has six sides and six vertices.

**(e) Heptagon:** (Hepta means seven) A heptagon has seven sides and seven vertices.

**(f) Octagon:** (Octa means eight) A octagon has eight sides and eight vertices.

**(g) Nonagon:** (Nona means nine) A nonagon has nine sides and nine vertices.

**(h) Decagon:** (Deca means ten) A decagon has ten sides and ten vertices.

**(i) n – gon:** A n-gon has n sides and n vertices. (Where n = 3, 4, 5, 6, ……..)

### Diagonals

A line segment which connects two non-consecutive vertices of a polygon is called diagonal. In this quadrilateral, AC and BD are diagonals. In the following pentagon, the diagonals are AC, AD, BE, BD and CE.

## Regular Polygon

An equilateral and equiangular polygon is called regular polygon. This means if a polygon has all angles equal and all sides equal, it is called regular polygon. For example: an equilateral triangle has all angles and sides equal, and hence is an regular polygon, A square is also a regular polygon.

## Irregular polygon

Polygon which has equal angles but not equal sides is called irregular polygon. For example: a rectangle has equal angles but no equal sides. So, it is an irregular polygon.

## Quardilateral

This is the combination of two Latin words; Quardi + Latus. Quadri – means four and Latus means side.

Hence, a polygon with four sides is called quadrilateral. Square, rectangle, rhombous, parellelogram, etc. are the examples of quadrilateral.

#### Angle sum property of a polygon:

Angle sum of a polygon `= (n – 2) xx 180⁰`

Where ‘n’ is the number of sides

**Example:**

A triangle has three sides,

Thus, Angle sum of a triangle `= (3 – 2) xx 180⁰ = 1 xx 180⁰ = 180⁰`

A quadrilateral has four sides,

Thus, Angle sum of a quadrilateral `= (4 – 2) xx 180⁰ = 2 xx 180⁰ = 360⁰`

A pentagon has five sides,

Thus, Angle sum of a pentagon `= (5 – 2) xx 180⁰ = 3 xx 180⁰ = 540⁰`

Similarly, angle sum of any polygon can be calculated.