Before we get into the different types of quadrilaterals, let’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. ∠A, ∠B, ∠C, and ∠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,

∠CAB + ∠B+ ∠BCA = 180° ….(1) ( angle sum property of a triangle)

similarly , in ADC,

∠CAD+ ∠D+ ∠DCA = 180° ….(2)

Adding (1) and (2), we get

∠CAB + ∠B + ∠BCA + ∠CAD + ∠D+ ∠DCA = 180° + 180°

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

So, ∠A + ∠B + ∠C + ∠D = 360°

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

Now let’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 180°

### Square:

- All sides are equal.
- All angles are equal of measure 90°
- 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 90°
- 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 180°
- 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