Quadrilateral: A quadrilateral is a plane figure enclosed by four sides. It has four sides, four interior angles and four vertices.

In quadrilateral ABCD, shown alongside: (i) four sides are : AB, BC, CD and DA. (ii) four angles are : ∠ABC,∠BCD, ∠CDA and ∠DAB ; which are numbered∠1, ∠2, ∠3 and ∠4 respectively. (iii) four vertices are : A, B, C and D.

Diagonals of a Quadrilateral : The line segments joining the opposite vertices of a quadrilateral are called its diagonals.

The given figure shows a quadrilateral PQRS with diagonals PR and QS. Types of Quadrilaterals : 1. Trapezium: A trapezium is a quadrilateral in which one pair of opposite sides are parallel.

The figure, given alongside, shows a trapezium as its sides AB and DC are parallel i.e. AB || DC. When the non-parallel sides of the trapezium are equal in length, it is called an isosceles trapezium. The given figure shows a trapezium ABCD whose non-parallel sides AD and BC are equal in length i.e. AD = BC; therefore it is an isosceles trapezium.

Also, in an isosceles trapezium :

(i) base angles are equal: i.e. ∠A = ∠B and ∠D =∠C (ii) diagonals are equal i.e. AC = BD.