Quadrilaterals come in different types. The most common types of quadrilaterals are a square, rectangle, rhombus, parallelogram, trapezium, and kite. Among these, many people get confused with rhombus and parallelograms and wonder if they are similar or if the terms are used interchangeably.
Rhombus and Parallelograms are different although they both have four sides and four vertices and look almost similar.
Rhombus vs Parallelogram
The main difference between rhombus and parallelogram is that a rhombus is a type of sloping four shaped figure having all sides equal, while a parallelogram is a type of sloping four shaped figure having opposite parallel sides equal.
However, the above is not the only difference. A comparison between both the terms on certain parameters can shed light on subtle aspects:
Comparison Table Between Rhombus and Parallelogram (in Tabular Form)
| Parameter of Comparison | Rhombus | Parallelogram |
|---|---|---|
| Meaning | Type of square having equal neighboring sides | Type of rectangle having parallel sides equal in length |
| Origination | From word “to turn round and round” | From word “Parallelogrammon” |
| Equality | All four sides will have the same length | Only opposite sides are equal in length |
| Similarity | Rhombus is very much similar to a square with the only difference being square is not in slanting position while rhombus is in a sloping position | Parallelogram is very much similar to a rectangle with the only difference being rectangle is not in slanting position while parallelogram is in a sloping position |
| Perimeter/ Circumference measurement | The perimeter of a rhombus is measured by formula 4a where “a” represents the side of the rhombus | The perimeter of a parallelogram is measured by the formula 2 (a+b) where “a” represents the side and “b” represents a base |
| Area Measurement | Area of rhombus is measured by formula (PQ)/2, where “p” and “q” represent the diagonals | Area of parallelogram is measured by formula bh where “b” represents base and “h” represents the height |
| Diagonals | Diagonals of a rhombus are at 90 degrees to each other at the intersection point | Diagonals of a parallelogram are not at 90 degrees to each other at the intersection point |
| Overall Scope | Rhombus can be considered as a Parallelogram | Every parallelogram cannot be considered as rhombus |
What is Rhombus?
Rhombus is derived from the Greek word “rhombos” and the verb “rhembō.” Rhombus is a concept that originated from Euclidean geometry. Rhombus in literal terms means something that whirls or spins around quickly.
Rhombus is a type of square because all the sides of a rhombus are equal. However, rhombus is a slanting (sloping) square. That means the sides are not at right angles. All rhombus cannot be considered as a square but vice versa can be true.
Rhombus has certain characteristics. The first one will be all sides will be equal in length. Secondly, the diagonal will cross each other at 90 degrees. Other features include opposite sides being parallel, opposite angles being equal, having 2 dimensions, and having a closed shape. Finally, adjacent angles will sum up to 180°.
Rhombus is also known as an equilateral quadrilateral or diamond. Rhombus can be considered as a type of parallelogram or a specific type of parallelogram as it fulfills the requirements of a parallelogram. In real-life scenarios, rhombus can be seen in a variety of aspects, the common one being a kite. Other things include building structure, ornament structure, and mirrors.
What is Parallelogram?
A parallelogram is a concept derived from Euclidean geometry. Parallelogram is derived from multiple words such as the French word ‘Parallelogramme’, Greek word Greek ‘Parallelogrammon’, and Latin word ‘Parallelogrammum’.
A parallelogram is a type of rectangle. A parallelogram means something which is surrounded by parallel lines. Parallelogram, where all the angles are perpendicular, will be considered as a rectangle.
The parallelogram has two pairs of parallel sides. The parallel sides are of equal length. The opposite angles of the parallelogram will be of equal measure. Parallelogram angles total to 180° and hence can be called as supplementary angles. An interesting feature of a parallelogram is that if one angle is right, then all angles will be in right position.
Parallelogram opposite sides are parallel and will never cross each other. The area of a parallelogram will be double the area of a triangle created by one of its diagonals. The diagonals of the parallelogram will cross each other at the middle point. Each diagonal will separate a parallelogram into two triangles which are identical in form.
Parallelogram area is measured by multiplying base into height. The perimeter which is the distance around the edges is measured by multiplying 2 into (base + side length). A parallelogram which has all sides congruent can be considered as a rhombus. A parallelogram that has all angles at right angles and the diagonals are equal will be considered as a rectangle. A parallelogram that has all sides equal sides with all angles perpendicular to each other can be considered as a square.
Main Differences Between Rhombus and Parallelogram
- Rhombus is a type of square. A parallelogram is a type of rectangle.
- Rhombus will have all the four sides equal in length. The parallelogram will only have opposite sides equal.
- Rhombus has all four sides parallel to each other. The parallelogram has only opposite sides parallel.
- The perimeter of the rhombus is measured by 4a and a=side. The perimeter of the parallelogram is measured by 2 (a+b) and a=side, b=base.
- Diagonals of the rhombus are perpendicular to each other at crossing points. Diagonals of the parallelogram are not perpendicular to each other at the crossing point.
- The area of the rhombus is measured by pq/2, where p and q are the diagonals. The area of the parallelogram is measured by bh where b= base and h= height.
Conclusion
The concepts of rhombus and Parallelograms are important for mathematics and science. Many theories are built on these foundation concepts. It is important for anyone in the geometry domain to have a solid and detailed study of these two structures to apply the same to complex mathematical models.
References
- https://qspace.library.queensu.ca/handle/1974/7650