Quadrilaterals Properties | Parallelograms, Trapezium, Rhombus

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.

Types of quadrilaterals

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

Parallelogram Properties

Properties of a parallelogram

  • Opposite sides are parallel and congruent.
  • Opposite angles are congruent.
  • Adjacent angles are supplementary.
  • 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

Rectangle Properties

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

Squares Properties

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

Rhombus Properties

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

Trapezium Properties

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

 
Continue learning more about:
Properties of Lines and Angles
Properties and formulas of Circles
Types of Triangles and Properties


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11 Comments

  1. Manav Madhwani says:

    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?

  4. Rakesh says:

    The angle of quadrilateral is sub set of quadrilateral ?
    my answer is no.
    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

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