Parallelogram: Definition of a Parallelogram, Basic Properties of a Parallelogram, Shape of a Parallelogram, Types of Parallelogram (For CBSE, ICSE, IAS, NET, NRA 2022)

Get unlimited access to the best preparation resource for NEST : fully solved questions with step-by-step explanation- practice your way to success.

Definition

  • A Parallelogram is a two-dimensional shape in sides are parallel to each other.
  • In Euclidean geometry, a parallelogram can be defined as a simple quadrilateral with two pairs of parallel sides.
  • In other words, we can define a parallelogram as a quadrilateral with two pairs of parallel sides.

Basic Properties of a Parallelogram

  • Total number of sides are four.
  • Total number of vertices are four.
  • Mutually parallel sides are two.
  • The opposite angles are congruent.
  • Area is equal to the multiplication of base and height.
  • Perimeter is twice the sum of adjacent sides length.
  • The sum of adjacent angles of a parallelogram is equal to 180 degrees.
  • The sum of all the interior angles equals 360 degrees.
A Parallelogram

In the above figure and

Also, we have and ; and

Since are supplementary and are supplementary,

and

Types of a Parallelogram

Rhomboid

  • The opposite pair of sides are parallel.
  • The opposite sides of a rhomboid are also congruent.
  • The diagonal divides the rhomboid into two congruent triangles.
  • The opposite angles of a rhomboid are also congruent.
  • The sum of interior angles of a rhomboid is equal to 360 degrees.
  • A rhomboid becomes a rhombus if all the sides become equal and therefore a rhombus is always a rhomboid.

Rectangle

  • A parallelogram with four angles of equal size (right angles) .
  • In a rectangle the diagonals are congruent.
  • The opposite sides are equal in a rectangle.
  • Each angle in the rectangle is the angle bisector of the opposite angle.

Rhombus

  • A parallelogram with four sides of equal length.
  • A rhombus is an equilateral quadrilateral.
  • An equilateral quadrilateral is one in which all the sides are equal.
  • In case of a kite, when all the sides become equal in length the kite becomes a rhombus.

Square

  • A parallelogram with four sides of equal length.
  • The angles of equal size (right angles) .
  • The diagonals are perpendicular bisectors of each other.
  • The lengths of the diagonals are equal.
  • All such squares in which the diagonals are congruent and bisect the angles are termed as parallelogram.
  • Every square is a rectangle and a rhombus.

Area of the Parallelogram

Area of the Parallelogram
A Parallelogram Can be Rearranged into a Rectangle

In the given parallelogram b is the base and h is the height and it can be divided into a trapezoid and a right triangle, Also in the second figure a parallelogram has been rearranged into a rectangle.

Therefore, the area of a parallelogram is the same as that of a rectangle with the same base and height

Area of the Parallelogram with Height H

In the above parallelogram the area is

Perimeter of Parallelogram

Perimeter = 2 (a + b) units