In this post we will try to classify quadrilaterals into different shapes and will also mention its associated properties.

## What are Quadrilateral shape ?

Quadrilateral is a 2 dimensional figures with four straight sides.

Let us understand the word “Quadrilateral”.

Lateral means “Sides”

Hence, it’s a shape containing four sides.

Consider the above quadrilateral ABCD.

Note it’s four sides AB, BC, CD and DA.
Understand the in Quadrilateral, the sides can be of different length.

Infact, we classify quadrilateral into different types on the basis of side length and angle measurement.

Let us understand shape of different form of quadrilateral.

### Square

It’s a quadrilateral in which all sides and angle are of equal measurement.
Note that in square, all angle measure 90 degrees.

Given above is the shape of quadrilateral named Square.

Since all sides are equal, we can write;
AB = BC = CD = DA

All angle measure 90 degree;
∠A = ∠B = ∠C = ∠D = 90 degree

Also note that in square, the opposite sides are parallel to each other.
AB || CD and AD || BC

In your surrounding, you will find various objects resembling the shape of square.

One common example of square shape object is chessboard. The board is made of 64 small squares and has all sides equal.

### Rectangle

It’s the quadrilateral in which opposite sides are of equal measurement.
Note that in rectangle, all angle measure 90 degrees.

Given above is the shape of quadrilateral named rectangle.

The rectangle has following properties;

(a) Opposite sides are equal
i.e. AB = CD and AD = BC

(b) Opposite sides are parallel to each other
AB || CD and AD || BC

(c) All angle measures 90 degrees
∠A = ∠B = ∠C = ∠D = 90 degree

(d) Diagonals are equal & bisect each other

In the above image of rectangle ABCD, AC and BD are the diagonals.

In rectangle, both the diagonals are equal.
AC = BD

In rectangle, diagonals bisect each other.
AO = OC and DO = OB

In real life there are objects like books, television, briefcase etc. that resembles the shape of rectangle.

Given above is the image of television set which resembles the shape of rectangle. Note that in above object, opposite sides are equal and all angles measure 90 degrees.

### Parallelogram

Parallelogram is a quadrilateral whose shape looked like a tilted square.

In parallelogram, opposite sides are equal and parallel.
Also, opposite angles are equal in this shape.

Given above is the shape of quadrilateral named parallelogram.

The parallelogram has following properties;

(a) Opposite sides are equal in length
i.e. AB = CD and AD = BC

(b) Opposite sides are parallel to each other
AB || CD and AD || BC

(c) Opposite angles are equal in measure
∠A = ∠C and ∠B = ∠D

(d) Diagonals of parallelogram are not equal but they bisect each other.

Given above is the image of parallelogram ABCD with diagonals AC and DB.

In parallelogram diagonals bisect each other.
i.e. AO = OC and DO = OB

(e) In parallelogram, the diagonal bisect each other into two congruent triangles.

Given above is the parallelogram ABCD with diagonal AC.
Here the diagonal AC divides the parallelogram into two congruent triangles name ABC and ADC.

(f) Parallelogram Law

The law states that the sum of square of all sides of parallelogram is equal to sum of square of diagonals.

For above parallelogram, the formula is expressed as follows;

\mathtt{AB^{2} +BC^{2} +CD^{2} +DA^{2} =\ AC^{2} +BD^{2}}

Please try to remember the formula, as the questions related to it are directly asked in exams.

### Rhombus

Rhombus is a quadrilateral whose shape looks like a diamond.

In Rhombus, all sides are equal.
Also, this is a quadrilateral in which opposite angles are equal.

Given above is the shape of quadrilateral named Rhombus.

Rhombus has following properties;

(a) All sides are equal
i.e. AB = BC = CD = DA

(b) Opposite angles are equal
∠A = ∠C and ∠B = ∠D

(c) Opposite sides are parallel to each other
AB || CD and AD || BC

(d) Diagonals bisect each other at right angle

Since in rhombus, the diagonals bisect each other, we can write;
AO = OC and DO = OB

Also, diagonals intersect at right angle.
∠AOB = 90 degree

(e) In rhombus, the diagonals bisect the angles
∠DAO = 1/2 ( ∠DAB )

(f) In Rhombus, when you join the midpoint of all sides, you will get a rectangle.

In the above figure, EFGH is the rectangle formed by joining midpoint of Rhombus sides.

Also the area of rectangle is half of the area of rhombus.

### Trapezium

It’s a quadrilateral in which one pair of opposite sides are parallel and other pair are not parallel.

Given above is the image of trapezium in which AB & CD are parallel sides and AD & BC are non parallel sides.

The parallel sides are generally referred as “Base”

The non- parallel sides are referred as “Legs”

Now the trapezium can be classified on the basis of length of sides;

(i) Isosceles Trapezium
It’s a trapezium in which both legs are of equal size.

(ii) Scalene Trapezium
It’s a trapezium in which all sides are of different length.

(iii) Right Trapezium
Trapezium in which pair of adjacent side angles are 90 degree.

Height of Trapezium
The height of trapezium can simply be found out by drawing straight line from one vertices to other side.

Popcorn bucket is one of the common example of trapezium shape that can be found in practical life.

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