In this tutorial on basic geometry concepts, we cover the types and properties of quadrilaterals: Parallelogram, rectangle, square, rhombus, trapezium.

#### Definition:

A quadrilateral is a simple closed figure with four sides.

There are five types of quadrilaterals.

• Parallelogram
• Rectangle
• Square
• Rhombus
• Trapezium

One common property of all quadrilaterals is that the sum of all their angles equals 360°.

Let us look into the properties of different quadrilaterals.

## Parallelogram

#### Properties of a parallelogram

• Opposite sides are parallel and congruent.
• Opposite angles are congruent.
• Diagonals bisect each other and each diagonal divides the parallelogram into two congruent triangles.
• If one of the angles of a parallelogram is a right angle then all other angles are right and it becomes a rectangle.

#### Important formulas of parallelograms

• Area = L * H
• Perimeter = 2(L+B)

## Rectangles

#### Properties of a Rectangle

• Opposite sides are parallel and congruent.
• All angles are right.
• The diagonals are congruent and bisect each other (divide each other equally).
• Opposite angles formed at the point where diagonals meet are congruent.
• A rectangle is a special type of parallelogram whose angles are right.

#### Important formulas for rectangles

• If the length is L and breadth is B, then

Length of the diagonal of a rectangle = √(L2 + B2)

• Area = L * B
• Perimeter = 2(L+B)

## Squares

#### Properties of a square

• All sides and angles are congruent.
• Opposite sides are parallel to each other.
• The diagonals are congruent.
• The diagonals are perpendicular to and bisect each other.
• A square is a special type of parallelogram whose all angles and sides are equal.
• Also, a parallelogram becomes a square when the diagonals are equal and right bisectors of each other.

#### Important formulas for Squares

• If ‘L’ is the length of the side of a square then length of the diagonal = L √2.
• Area = L2.
• Perimeter = 4L

## Rhombus

#### Properties of a Rhombus

• All sides are congruent.
• Opposite angles are congruent.
• The diagonals are perpendicular to and bisect each other.
• Adjacent angles are supplementary (For eg., ∠A + ∠B = 180°).
• A rhombus is a parallelogram whose diagonals are perpendicular to each other.

#### Important formulas for a Rhombus

If a and b are the lengths of the diagonals of a rhombus,

• Area = (a* b) / 2
• Perimeter = 4L

## Trapezium

#### Properties of a Trapezium

• The bases of the trapezium are parallel to each other (MN ⫽ OP).
• No sides, angles and diagonals are congruent.

#### Important Formulas for a Trapezium

• Area = (1/2) h (L+L2)
• Perimeter = L + L1 + L2 + L3

## Summary of properties

Summarizing what we have learnt so far for easy reference and remembrance:

 S.No. Property Parallelogram Rectangle Rhombus Square 1 All sides are congruent ✕ ✕ ✓ ✓ 2 Opposite sides are parallel and congruent ✓ ✓ ✓ ✓ 3 All angles are congruent ✕ ✓ ✕ ✓ 4 Opposite angles are congruent ✓ ✓ ✓ ✓ 5 Diagonals are congruent ✕ ✓ ✕ ✓ 6 Diagonals are perpendicular ✕ ✕ ✓ ✓ 7 Diagonals bisect each other ✓ ✓ ✓ ✓ 8 Adjacent angles are supplementary ✓ ✓ ✓ ✓

Properties of Lines and Angles
Properties and formulas of Circles
Types of Triangles and Properties

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Very simple and easy to learn from this website
Thanks!!

2. Sophie says:

Do opposite sides in a quadrilateral have to be equal in order for it to have diagonals that are perpendicular?

• Maryam says:

Yes when sides on opposite are equal then only the diagnols perpendicularly bisect each other

• K.K.Mukherjee says:

It is not correct.The diagonals are perpendicular if and only if all the sides are equal as in the case of a rhombus or a square.
The diagonals will be perpendicular also if the pairs of adjacent sides are equal as in the case of a kite

3. Piyush says:

Are the measure of a pair of parallel sides in a trapezium equal?

• Harish says:

No they are not.
If they were, it would become a parallelogram and a trapezium is not a parallelogram

4. Rakesh says:

but still not get whole explanation.
pls explain

5. Nightwing says:

You Forgot one Quadrilateral : Kite

6. GAYATRI says:

In trapezium only one pair of opposite sides are parallel

7. anonymous says:

are the diagonals of the rectangles are congruent?
how to proof it?

• Gurleen says:

Take a triangle with common base from that dignols and made that triangle congruent by sas then both side will be equal by cpct