Lesson Different types of parallelogram

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In this lesson we will learn what is a parallelogram, how to identify a parallelogram, what are different types of parallelogram and properties associated with them.

Before looking into different types of parallelogram we should first try to understand what is a parallelogram.

What is a Parallelogram ?

drawing( 160, 160, -10, 10, -10, 10, line( -6, -6,4,-6) , line( -6, -6,-2,2), line( -2, 2,8,2) , line( 8, 2,4,-6),line( -6, -6,8,2) ,line( -2, 2,4,-6) ,locate( -6.5,-6.5,A),locate( 4.5,-6.5,B),locate( 8.5,3.5,C),locate(-2.5,4,D),locate(-0,-2.4,O))

In simplest terms a parallelogram is defined as a four-sided plane figure with opposite sides parallel. It is a close bound figure as shown in figure. Parallelogram differs from a quadrilateral because it has following special properties.

How to identify a parallelogram?

If any one of the following conditions takes place then we can call that quadrilateral a parallelogram:

1. If in a quadrilateral, there are two pairs of parallel sides, then it will be a parallelogram.

2. If in a quadrilateral, two pairs of opposite sides are of the same lengths, then it will be a parallelogram.

3. If in a quadrilateral, two pairs of opposite angles are same, then it will be a parallelogram.

4. If in a quadrilateral, the diagonals bisect each other, then it will be a parallelogram.

5. If in a quadrilateral, one pair of opposite sides which are parallel and equal in length, then it will be a parallelogram.

Properties of a parallelogram:

The properties associated to a parallelogram which will be true in all types of parallelogram are as follows:

1. Opposite sides are equal (AB=CD, AD=BC).

2.Opposite angles are equal (A=C, B=D).

3. Two opposite sides are equal and parallel (AB=CD, AB||CD).

4. Diagonals are divided in their intersection point into two (AO=OC, BO=OD).

Types of parallelogram:

The parallelogram are of following types according to some special properties associated to each one of them.


1. Square :

drawing( 160, 160, -10, 10, -10, 10, line( -6, -6,4,-6) , line( -6, -6,-6,4), line( -6, 4,4,4) , line( 4, 4,4,-6) ,locate( -6.5,-6.5,A),locate( 4.5,-6.5,B),locate( 4.5,4.5,C),locate(-7.5,5,D))

A square is a special type of parallelogram. The properties associated to a square are:

1. All sides are equal in length.

2. Each angle in a square is 90 degrees.

3. Diagonals of square bisect each other at right angles.

4. The area of square is square of side.

2. Rectangle :

drawing( 160, 160, -10, 10, -10, 10, line( -6, -6,4,-6) , line( -6, -6,-6,1.5), line( -6, 1.5,4,1.5) , line( 4, 1.5,4,-6) ,locate( -6.5,-6.5,A),locate( 4.5,-6.5,B),locate( 4.5,2.5,C),locate(-7,3,D))

1. Opposite sides are equal in length.

2. Each angle in a rectangle is 90 degrees.

3. The diagonals of rectangle bisect each other at right angles.

4. The area of rectangle is product of length and breadth.

3. Rhombus :

drawing( 160, 160, -10, 10, -10, 10, line( -6, -6,4,-6) , line( -6, -6,-1.29,3.42), line( -1.29, 3.42,8.71,3.42) , line( 8.71,3.42,4,-6),line( -6, -6,8.71,3.42) ,line( -1.29,3.42,4,-6) ,locate( -6.5,-6.5,A),locate(4.5,-6.5,B),locate( 9,4.5,C),locate(-2.3,5.3,D))

1. All sides are equal in length.

2. No angle is equal to 90 degrees.

3. The diagonals bisect each other and intersect at right angles.

4. The area of a rhombus is product of base and height of the perpendicular.

To learn how to distinguish between different type of parallelogram refer to link
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