Before we get into the different types of quadrilaterals, letâ€™s define what a quadrilateral is? what are the properties of it and also the properties of the types of quadrilaterals?

## What are quadrilaterals??

A quadrilateral is a simple closed figure bounded by four line segments in a plane.

The quadrilateral ABCD has four sides AB, BC, CD, and DA, four vertices are A, B, C, and D. âˆ A, âˆ B, âˆ C, and âˆ D are the four angles formed at the vertices.

When we join the opposite vertices A, C, and B, D. AC and BD are the two diagonals of the quadrilateral ABCD.

### Properties of a quadrilateral:

There are four angles in the interior of a quadrilateral. Can we find the sum of these four angles? Let us recall the angle sum property of a triangle. We can use this property in finding the sum of four interior angles of a quadrilateral.

ABCD is a quadrilateral and AC is a diagonal.

We know the sum of the three angles of ABC is,

âˆ CAB + âˆ B+ âˆ BCA = 180Â° â€¦.(1) ( angle sum property of a triangle)

similarly , in ADC,

âˆ CAD+ âˆ D+ âˆ DCA = 180Â° â€¦.(2)

Adding (1) and (2), we get

âˆ CAB + âˆ B + âˆ BCA + âˆ CAD + âˆ D+ âˆ DCA = 180Â° + 180Â°

Since âˆ CAB + âˆ CAD = âˆ A and âˆ BCA + âˆ DCA = âˆ C

So, âˆ A + âˆ B + âˆ C + âˆ D = 360Â°

i.e; the sum of four angles of a quadrilateral is 360Â° or 4 right angles.

Now letâ€™s get into 6 differents:

## Different Types of Quadrilaterals:

- Parallelogram
- Square
- Rectangle
- Rhombus
- Trapezium
- Kite

### Parallelogram :

- A quadrilateral with both pairs of opposite sides are parallel and equal
- Opposite angles are equal
- Diagonals bisect each other.
- The Sum of adjacent angles is 180Â°

### Square:

- All sides are equal.
- All angles are equal of measure 90Â°
- Opposite sides are parallel to each other.
- Both diagonals are equal and bisect each other.
- Diagonals are perpendicular to each other.

### Rectangle:

- Opposite sides are equal.
- Adjacent sides are perpendicular to each other.
- All angles are equal and of measure 90Â°
- Both diagonals are equal and bisect each other.
- Opposite sides are parallel to each other.

### Rhombus :

- All sides are equal.
- Opposite angles are equal.
- Diagonals bisect and perpendicular to each other.
- The sum of the adjacent angles is 180Â°
- Opposite sides are parallel to each other.

### Trapezium:

- One pair of opposite side are parallel to each other.

### Kite :

- Two pairs of consecutive sides are equal.
- Diagonals are perpendicular to each other.
- One of the diagonal bisect each other.

Differences between Rational numbers and Irrational numbers