A quadrilateral is a polygon which has 4 vertices and 4 sides enclosing 4 angles. The sum of its interior angles of a quadrilaterl is 360 degrees. We can also derive the sum of interior angle from the formula of polygon i.e. $$\mathbf{(n-2) \times 180}$$..

A quadrilateral, in general, has sides of different lengths and angles of different measures. However, squares, rectangles, etc. are special types of quadrilaterals with some of their sides and angles being equal. In this article, we will discuss the special types of quadrilaterals and their basic properties.

• Trapezium: It is a quadrilateral with one pair of opposite parallel sides. In the trapezium ABCD, side AB is parallel to side CD.

• Parallelogram: It is a quadrilateral with two pairs of parallel sides. The opposite sides are parallel and equal in length. The opposite angles are equal in measure. In the parallelogram ABCD, side AB is parallel to side CD and side AD is parallel to side BC.
Also, the two diagonals formed intersect each other at the midpoints. As in the figure given below, E is the point where both the diagonals meet. So
Length AE = EC, & Length BE = ED

• Rectangle: It is a quadrilateral with all the 4 angles of equal measure, that is, each of them is 90°. Both the pairs of opposite sides are parallel and equal in length.

• Rhombus: It is a quadrilateral with all the four sides having equal lengths. The Opposite sides of a rhombus are parallel and opposite angles are equal.

• Square: It is a quadrilateral in which all the sides and angles are equal. Every angle is a right angle (i.e. 90° each). The pairs of opposite sides are parallel to each other.

• Kite: It is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.

• Square, rectangle and rhombus are types of parallelograms.
• A square is a rectangle as well as a rhombus.
• Rectangle and rhombus are not a square.
• A parallelogram is a trapezium.
• A trapezium is not a parallelogram.
• Kite is not a parallelogram.

Quadrilateral is a 4 sided polygon bounded by 4 finite line segments.The word ‘quadrilateral’ is composed of two Latin words, quadri meaning ‘four ‘and latus meaning ‘side’. It is a two dimensional figure having four sides (or edges) and four vertices.

A quadrilateral has 2 diagonals based on which it can be classified into concave or convex quadrilateral. In case of convex quadrilaterals, diagonals always lie inside the boundary of the polygon.

The basic types of quadrilaterals are:

1.Trapezium

2.Parallelogram

• Rectangle
• Rhombus
• Square

3.Kite

This could be better understood with help of following figure.

As shown in the above figure:

Trapezium is a quadrilateral which has one pair of parallel sides. The parallel sides are known as base of quadrilateral.

Parallelogram is a quadrilateral in which opposite sides are parallel and equal to each other.

Two special types of parallelogram are rectangle and rhombus. A parallelogram which has all four sides of equal measure and diagonals are perpendicular bisectors of each other is known as a rhombus. Rectangle is a special case of parallelogram in which each interior angle measures $$90^{\circ}$$.

Square is a parallelogram which has properties of both a rhombus and a rectangle.  A square is basically described as a parallelogram having all sides of equal measure and each of the interior angles measuring . Kite is a quadrilateral in which two pairs of adjacent sides are of equal length and the diagonals intersect each other at right angles.

We can sum up the properties of a quadrilateral as given below:

• They have 4 sides (or edges)
• They have 4 vertices (or corner points)
• Their internal angles add up to a total of $$360^{\circ}$$
• The measure of sum of exterior angles of a quadrilateral is $$360^{\circ}$$<

Using Venn-Diagrams also, the  relationship between different types of quadrilaterals can be shown as follows:

#### Practise This Question

A quadrilateral with two distinct pairs of equal-length adjacent sides is known as