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Difference Between Rhombus and Parallelogram

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Last updated date: 23rd Jul 2024
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Quadrilaterals: Rhombus and Parallelogram

A quadrilateral is a polygon with four sides. To recall, the word ‘quad’ means four and the word ‘lateral’ means sides i.e. a quadrilateral is a figure bounded by four line segments such that no three of them are parallel to each other. A quadrilateral has four sides, four vertices, and four angles. 

 

Rhombus and parallelogram are also considered quadrilaterals as they possess the basic property of quadrilaterals. But are these two shapes different from each other? Let’s find out the difference between a parallelogram and a rhombus in this article. 

What is a Rhombus?

Rhombus is a four-sided two-dimensional quadrilateral with all its four sides equal in lengths. Rhombus is also referred to as a slanting square. Opposite sides of a rhombus are parallel. Rhombus is also called an equilateral quadrilateral, a diamond or a lozenge. 

 

The properties of square and rhombus are similar, but the main distinguishing property is that square has all the angles equal to 90o, and rhombus does not. Also, all rhombus are not squares but all squares are rhombus. 

 

Some of the important properties of a rhombus are as follows:

  • The diagonals of a rhombus bisect each other and are perpendicular (forms right angle). They form scalene triangles. 

  • Opposite angles of the rhombus are equal and a diagonal bisects the internal angles.

  • Adjacent sides are equal in lengths.

Consider the below figure of a rhombus we have,

 

(Image will be uploaded soon)

 

  • Sides AB = BD = DC = CA

  • Diagonal ADCB

  • Angle CAB = angle BDC and angle ACD = angle ABD 

  • As diagonal AD and BC bisects the opposite angles, so angle ABC = angle CBD and angle BCD = angle BCA

What is a Parallelogram?

A parallelogram is a four-sided two-dimensional quadrilateral whose opposite sides are parallel and congruent to each other. A parallelogram is also referred to as a slanting rectangle. Opposite interior angles of a parallelogram are of equal measures. The parallelogram and a rectangle are near about the same with one distinguishing property that the rectangle has all the angles of 900 while parallelogram does not. This means that all rectangles are parallelograms but the vice versa is not true.

 

Some of the important properties of a parallelogram are:

  • Opposite sides are of equal length and are parallel to each other.

  • Diagonals bisect the opposite angles. 

  • Diagonals bisect each other.

  • Each diagonal bisects the parallelogram in two equal triangles.

Consider the below figure of a parallelogram we have,

 

(Image will be uploaded soon)

 

  • Side AC = side BD and side AB = side CD

  • Side AB ∥ side CD and side AC ∥ side BD

  • Angle CAB = CDB and angle ACD = angle ABD

  • Diagonal AD bisects diagonal BC

  • Diagonal BC bisects parallelogram in two equal triangles △ABC = △BCD

  • Diagonal AD bisects parallelogram in two equal triangles △ ACD =△ABD

Difference Between Rhombus and Parallelogram 

Rhombus and parallelograms are closely related to each other but they are still different. They are two different quadrilaterals. Some of the key difference between rhombus and parallelogram in the tabular form are:

Rhombus Vs Parallelogram

Sr. No

Rhombus

Parallelogram

1

It is a 2-D figure with equal neighboring sides.

It is a 2-D figure with equal parallel sides.

2

All the four sides are of equal lengths. 

Opposite sides are of equal lengths.

3

The area of rhombus is given by  \[\frac {d_1 \times d_2}{2}\], where d1 and d2 are its diagonals.

The area of a parallelogram is given by bh, where b and h are its base and height respectively.

4

The perimeter of a rhombus is equal to P = 4a, where “a” is the length of each side.

The perimeter of a parallelogram is equal to, given, P = 2 (a+b), where “a” is the side and b is the base.

5

Diagonals bisect each other at right angle, forming two scalene triangles

Diagonals bisect each other, forming congruent triangles


6

Every rhombus is a parallelogram

Every parallelogram is  not a rhombus

7

The term rhombus has originated from the Latin word with the meaning “to turn round and round.”

The term parallelogram has originated from the Greek word “parallelogram” with the meaning “parallel lines”.

How to Identify Whether a Quadrilateral is a Rhombus or a Parallelogram?

This is an obvious question every student has in their mind. To identify the nature of a quadrilateral, there are a few things we need to observe and do.

  • First of all, measure the length of all sides. If the length of all sides are the same, it may be a square or rhombus, but never a parallelogram. 

  • Now check the diagonals if they bisect each other at right angles, and make the conclusion accordingly

  • Last thing is to check the opposite angles. 

Considering all these things, you can conclude your answer with proper justification.

Conclusion

Thus, we conclude that a rhombus is a special kind of parallelogram and that every rhombus can be a parallelogram but not vice versa. This is because in addition to parallel sides, rhombus also has all the sides equal, whereas in parallelogram opposite sides are parallel but adjacent sides size may not be the same.

FAQs on Difference Between Rhombus and Parallelogram

1. What is Rhombus?

Rhombus is a four-sided quadrilateral with all its four sides equal in lengths. Rhombus is also referred to as a slanting square. Opposite sides of a rhombus are parallel. The properties of square and rhombus are similar, the only distinguishing property is that square has all the angles equal to 900, and rhombus does not.


Rhombus is also called an equilateral quadrilateral. Also called a diamond or a lozenge. Every rhombus is a parallelogram but the vice versa is not true.


(Image will be Uploaded Soon)


2. What is Parallelogram?

A parallelogram is a four-sided quadrilateral whose opposite sides are parallel and congruent to each other. A parallelogram is also referred to as a slanting rectangle. Opposite angles of a parallelogram are of equal measures. The parallelogram and a rectangle are near about the same with one distinguishing property that the rectangle has all the angles of 900 and that of parallelogram does not.


(Image will be Uploaded Soon)


3. Is a Square a Rhombus?

  •  Rhombus is a quadrilateral with all of its four sides of equal lengths. And a square is also a quadrilateral with all its four sides of equal lengths, but the internal angles of a square are 900. thus a rhombus is not a square unless its internal angle is 900

  • Also the lengths of squares are of equal lengths. And that of a rhombus are of unequal lengths.

  • All angles of a square are equal and measure 900, whereas only opposite angles of a rhombus are of equal measures.

4. Is Trapezoid a Parallelogram?

No, a trapezoid is not a parallelogram. Because trapezoid is defined as a quadrilateral with one pair of parallel sides and one pair of non-parallel sides. While parallelograms have two pairs of parallel sides. Also opposite angles of a parallelogram are equal and that of the trapezoid is unequal.

5. How is rhombus different from a square?

Square

Rhombus

All the angles are equal. 

Only the opposite angles are equal to each other.

Each angle should be 90°.

Angles need not measure 90°.

Both the diagonals are equal in length.

The diagonals are of unequal length.

Its sides are perpendicular to each other.

Its sides need not necessarily be perpendicular to each other.

There are four lines of symmetry.

There are two lines of symmetry.

It can be inscribed in a circle

It cannot be inscribed in a circle.

6. Is trapezoid a parallelogram?

No, a trapezoid is not a parallelogram. This is because a trapezoid is defined as a quadrilateral with one pair of parallel sides and one pair of non-parallel sides. While parallelograms have two pairs of parallel sides. Also opposite angles of a parallelogram are equal and that of the trapezoid are unequal.