Class 8 Maths

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.

triangle quadrilateral

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

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

pentagon hexagon

(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.

heptagon octagon

(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.

nonagon decagon

(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.

diagonals of a quadrilateral diagonals of a pentagon

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.

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.

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.