Types of Parallelogram

Geometry

Properties of parallelogram and its Types

A parallelogram is a special kind of quadrilateral in which both pairs of opposite sides are parallel. In fig. 1 given below, AD||BC and AB||CD .

Figure 1: Parallelogram

The four basic properties of parallelogram are:

• Opposite sides of a parallelogram are equal
• Opposite angles of parallelogram are equal
• Diagonals divide the parallelogram into two congruent triangles
• Diagonals bisect each other

There are three special types of parallelogram, they are:

• Rectangle
• Rhombus
• Square

Let us discuss these special parallelograms one by one.

Rectangle:

Rectangle is a special case of parallelogram in which measure of each interior angle is

The path which surrounds a two-dimensional object is known as its perimeter. The two-dimensional space occupied by an object is known as its area. A rectangle with length l units and breadth as b units has perimeter equal to  2( l + b) units and its area is equal to

Figure 2: Rectangle

Fig. 2 shown above represents a rectangle in which all angles are right angles and opposite sides are equal.

Since a rectangle is a parallelogram, it inherits all the properties of parallelogram along with some special properties which differentiates it from other parallelograms:

Properties of rectangle:

• Measure of each interior angle is
  \(\begin{array}{l} 90^\circ \end{array} \)
• Opposite sides are equal
• Diagonals are congruent
• Each diagonal is angle bisector of opposite angle

Rhombus:

A parallelogram in which all four sides are equal in length is known as a rhombus.  A rhombus is an equilateral quadrilateral. By equilateral quadrilateral, we mean a quadrilateral with all sides equal.  Every rhombus is a parallelogram since it has both pairs of opposite sides parallel. When all the sides of a kite become equal in length, then that kite becomes a rhombus as sides are of equal length and diagonals are perpendicular to each other. Hence, every rhombus is also a kite.

Figure 3: Rhombus

Fig. 3 represents a rhombus with sides AB = BC = CD = DA and diagonals intersecting at right angles.

Since a rhombus is a parallelogram, all the properties of a parallelogram are applicable to it.

Properties of Rhombus:

• All sides are congruent
• Diagonals bisect each other at right angles
• Opposite angles are equal and each diagonal is angle bisector of opposite angle

Geometrically, polygons are related with their duals i.e. vertices of one polygon correspond to sides of another polygon. Rhombus is the dual polygon of rectangle and vice- versa. By joining mid points of sides of rectangle a rhombus is formed and vice-versa. This could be understood through the table given below:

Table1: Duality of Rectangle and Rhombus

Square:  A parallelogram which has properties of both a rhombus and a rectangle.  A square is a parallelogram with equal sides and one of its interior angles as right angle.

Figure 4: Square

Fig. 4 depicts a square in which measure of each interior angle is

Properties of Square:

• All sides are equal in length
• Each interior angle is right angle
• Length of diagonals is equal
• Diagonals are perpendicular bisectors of each other
• Every square is a parallelogram in which diagonals are congruent and bisect the angles
• Every square is a rectangle and a rhombus

Here are different types of Parallelogram and their properties. For more on parallelograms watch the video.’