## Properties of Quadrilaterals

A quadrilateral is simply a 2-dimensional geometrical figure consisting of "four sides". The term quadrilateral is derived from two words i.e. quad = four and lateral = side. A Quadrilateral is a closed, flat shape in which the lines connect, and has straight sides.

Talking about the properties of a quadrilateral, these are as follows:

A polygon with four straight sides also termed as edges

it has four vertices also termed as corners

A quadrilateral has four interior angles that sums up to 360 degrees

### What is a Quadrilateral Shape?

A Quadrilateral is a polygon of 2D geometrical figures consisting of "four sides". A quadrilateral can sometimes also be known as:

Quadrangle derived from 2 words i.e. quad meaning ("four angles"), and rangle that sounds like "triangle"

Tetragon derived from 2 words i.e. ("four polygon"), and gon that sounds like "hexagon", "pentagon", octagon etc.

### Types of Quadrilaterals and Their Properties

There are various special kinds of quadrilateral. The Quadrilaterals and its classification are as below.

(Image to be added soon)

### Paralleogram

A parallelogram is a simple quadrilateral under the Euclidean geometry in which both pairs of opposite sides are parallel to one another. A parallelogram also consists of the following properties:

Opposite sides of a parallelogram are congruent

Opposite angles are in congruence

Adjacent angles are supplementary, meaning that they make 180 degree measurement

The diagonals intersect each other.

### Rectangle

A rectangle is one form of a parallelogram only. Since a rectangle has four right angles, thus all rectangles are also parallelograms and quadrilaterals. On the contrary, not all parallelograms and quadrilaterals are rectangles. A rectangle consists of the following properties:

Opposite sides are in congruence

Opposite angles are in congruence

Adjacent angles are supplementary, meaning that they make 180 degree measurement

The diagonals intersect each other.

The diagonals are in congruence

### Square

A square is a 2 dimensional, closed geometric object consisting of 4 equal sides. A Square is most frequently seen around us in real life in the form of a wall clock, chessboard, bread slice etc. A square consists of the following properties:

A square consists of 4 sides and 4 angles

Length of all the sides of a square are equal in measurement

All angles are at right angles and are 90 degrees each

All interior angles are equal in measurement and the sum of all the interior angles is 360°.

A square can be described as a rhombus which is also a rectangle – specifically, a parallelogram with 4 congruent sides and 4 right angles.

### Rhombus

A rhombus is a parallelogram with four sides in congruence to each other. Rhombus is also known as rhombi in its plural sense. A rhombus also consists of the following properties:

Opposite sides of a rhombus are congruent

Opposite angles are in congruence

Adjacent angles are supplementary, meaning that they make 180 degree measurement

The diagonals bisect each other at right angles.

In some textbooks you will find a kite has a minimum of 2 pairs of adjacent congruent sides, thus a rhombus is a special case of a kite.)

### Trapezoid

A trapezoid is a unique kind of a quadrilateral that has exactly one pair of parallel sides. There may be some ambiguity with respect to this term depending on the country you're from. This is to say, in India and Britain, they call it trapezium; whereas, in America, trapezium generally means a quadrilateral polygon with no parallel sides.)

### Isosceles Trapezoid

An isosceles trapezoid is kind of a trapezoid whose non-parallel sides are in congruence to each other. A kite is one type of a quadrilateral consisting of exactly two pairs of adjacent sides congruent. This description of a quadrilateral shape excludes rhombi.

1. What are a scalene quadrilateral and its properties?

A scalene quadrilateral is simply a 4 -sided polygon which consists of no sides congruent. Below shown are the examples of a scalene triangle:

(Image to be added soon)

2. What is an irregular quadrilateral?

irregular Quadrilaterals are the polygon shapes whose sides and angles are not equal in measurement. So wondering, what is a regular quadrilateral? The only regular i.e. a geometric polygon having all sides and all angles equal is a regular quadrilateral. The only regular quadrilateral is a square. That said, all other remaining quadrilaterals are irregular.

3. What do we understand by Complex Quadrilaterals?

We call a quadrilateral as a complex quadrilateral when its two sides cross over. In other words, it is also referred to as a "Self-Intersecting" quadrilateral.

4. What is a polygon?

A polygon is a plane geometrical figure illustrated by a countless number of straight line segments joined to form a polygonal circuit or a closed polygonal chain. A quadrilateral is a polygon, in fact, a four-sided polygon, just how a triangle is a three-sided polygon, a pentagon is a five-sided polygon, and a heptagon is a seven-sided polygon, and so on.