Rhombus and Parallelogram

Rhombus and Parallelogram are two corner-based geometric shapes. They can be seen as parallelograms that are shifted towards one another. The main difference between the two shapes is that in rhombus, the edges are parallel whereas, in a parallelogram, they are not.

Rhombus and Parallelogram: History and Definition

Rhombus was first introduced by Euclid in his book of geometry; ‘Elements’. His definition was- “an equilateral parallelogram” He defined it as a rhombus. Parallelogram was first described by Euclid’s disciple Eudoxus around 350 B.C. It is seen as a triangle whose opposite sides have been cut at the same angle (a diagonal).

What is Rhombus?

The shape which is obtained if all the diagonals of a parallelogram are made equal is called a rhombus. The word “rhombus” comes from the Greek word ‘Rhombus’ which means “diamond shape” or “spiked”.

It has 4 sides and these are all equal both in length and breadth. All the angles in the rhombus are right angles.

Rhombus is used to describe the shape of some battleships and airplanes etc.

Characteristics of Rhombus:

1) In the rhombus, the diagonals are equal in length or breadth.

2) The diagonals of a rhombus are equal and concurrent.

3) Rhombus is also known by its synonym ‘Quadrilateral’.

4) Rhombus has four equal sides and four equal angles.

5) The shortest side of the rhombus is called ‘Shortest Distance’ (MD). 

6) The midpoint of the diameters of the rhombus lies on MD. 

7) The opposite sides of a parallelogram bisect each other; thus, their ratio is a perfect square. While for rhombus, their ratio is never a perfect square.

What is Parallelogram?

A parallelogram has 2 pairs of parallel sides. The opposite sides are not equal in length whereas both diagonals bisect each other at 90 degrees angles (right angles).

Some of the applications of a parallelogram are-

(1) Parallelogram is the length of a triangular window in a building. When the diagonal is said to be “the height” then this is called “Rhombus”.

(2) In-home windows, the diagonal which splits each pane into 2 halves is termed as “Rhombus” and that which covers only one half of each pane is termed as “Rectangle”.

Characteristics of Parallelogram:

1) The diagonals in a parallelogram are parallel and they bisect each other at 90 degrees angle.

2) The sides of the parallelogram are not equal.

3) In the right angle triangle, the angles opposite to each other are equal and right angles. But, in a parallelogram, these two angles opposite to each other are unequal and obtuse (if acute then it is a trapezoid). This makes it difficult to determine if it is Rhombus or Parallelogram.

What are the differences between Rhombus and Parallelogram?

1) Rhombus is a rhomboidal shape whereas Parallelogram is an absolute rectangle.

2) The diagonals of a rhombus are equal and concurrent whereas in parallelogram they are unequal and non-contiguous.

3) In a rhombus, the shortest side is always given as MD and the diagonal bisects bisector of MD. In a parallelogram, it never bisects MD. 

4) In Rhombus all the angles are right but in Parallelogram, all the angles are not right.

5) In Rhombus, all the sides are equal in length and breadth but in Parallelogram, the opposite sides are not equal in length.

6) The midpoint of the diameters of a Rhombus lie on MD but in Parallelogram this is never so.

7) In Rhombus, all opposite angles are right angles but in a parallelogram, all opposite angles aren’t right angles.

8) The ratio of opposite sides is always a perfect square but it is never so for Rhombus.

9) The length of the diagonal is 2 times its width while that of the rhombus diagonal is not equal to 2 times its width.

Conclusion:

As compared to Rhombus, Parallelogram is a rectangle that has opposite sides parallel to each other and they are not parallel to each other at the same time. Thus, we can say that the difference between Rhombus and Parallelogram is more than the similarities. It can be concluded that Rhombus is a parallelogram but not exactly a Parallelogram.