A quadrilateral is a polygon of 4 sides. In other words, a quadrilateral is a closed plane figure with four sides. The line segments AC and BD are its diagonals.
The classification of quadrilaterals is summarised below :

1.    Parallelogram
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.
In the given figure, side AB is parallel to DC and side BC is parallel to AD or also we can write as AB || DC, AD || BC, therefore ABCD is a parallelogram. 2.    Rectangle
A rectangle is a parallelogram, whose all angle is a right angle.
In the given figure, ABCD is a rectangle. 3.    Rhombus
A rhombus is a parallelogram whose all sides are equal.
In the figure, PQRS is a parallelogram in which PQ = QR = RS = SP.
Diagonals PR and QS bisect each other at 90°. 4.    Square
A square is a parallelogram whose all sides are equal and each angle are right angle.
In the given figure, AB = BC = CD = DA and A = B =C =D = 90°. 5.    Trapezium
A trapezium is a quadrilateral with only one pair of opposite sides parallel.
In the given figure, ABCD is a trapezium in which AB || DC. 