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


Liked the article? Show us some love. Share it.

MBA Crystal Ball provides professional Admissions Consulting services. Hire us to improve your chances of getting into the top international universities. Email: info [at] mbacrystalball [dot] com

MBA Crystal Ball //
MBA Crystal Ball
Our counsellors can help you with career counselling and admissions consulting. Check out our free resources for: GMAT Preparation & GMAT Syllabus | MBA Subjects | MBA Scholarships | And much more

5 Comments

  1. Manav Madhwani says:

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

  2. Arshdeep Singh Dhotian says:

    Very simple and very good examples

  3. Daksh patel says:

    Nice explaination

    Easy To Understand

    THANK YOU

  4. ADITYA SAHA says:

    Very easy to understand and very nice

  5. Sophie says:

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

Leave a Reply

Your email address will not be published. Required fields are marked *