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.


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 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)


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 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 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 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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  1. 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

    • Sid says:

      No all sides of a quadrilateral should be congruent for the diagonals to be perpendicular

  2. Piyush says:

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

  3. Nightwing says:

    You Forgot one Quadrilateral : Kite

  4. anonymous says:

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

    • Anil says:

      Since the opposite sides of a rectangle are congruent, it’s diagonals are also congruent. This can be done by applying Pythagoras theorem..

    • 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

  5. Grreshma says:

    If ab =33 bc =27 CD = 33 DA=21 area of quadrilateral ?

    • Simron says:

      Area of the quadrilateral = Area of rectangle + Area of Right angled triangle
      Length of the rectangle = 33cm
      Breadth of the rectangle = 21cm
      Area of rectangle = Length x Breadth
      = 33 x 21
      = 693 sq. cm
      Now in right angled triangle,
      Hypotenuse = 33cm
      Base = 6cm
      Therefore, the height of the triangle = Square root of (square of hypotenuse – square of base) [ By Pythagoras Theorem ]
      = Square root of(33 x 33 – 6 x 6)
      = Square root of 1053
      = 32.44cm
      Area of Right angled Triangle = 1/2 x base x height
      = 1/2 x (27-21) x 32.44
      = 1/2 x 6 x 32.44
      = 97.32 sq. cm

      So, Area of the quadrilateral = Area of rectangle + Area of Right angled triangle
      = 693 + 97.32
      = 790.32 sq. cm

    • Saurabh says:

      Why are you asking because it is quite easy?

      You know that when the heights of quadrilateral are given which will perpendicular to any one of diagonal then fomula for area is given by

  6. Kevin says:

    What are the names of the three different quadrilaterals with two congruent

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