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.

trianglequadrilateral

(b) Quardilateral: A quardilateral has four sides and consequetively 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

x(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.

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


Diagonals

A line segments which connects two non-consecutive vertices of a polygon is called diagonal.

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 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 not equal sides, and hence 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. In quadrilateral, sides are straight and are of two dimensional. 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 os 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.


Ex 3.1

Ex 3.2

Ex 3.3

Ex 3.4

Quadrilateral Extra Questions