A rhombus and a parallelogram are both types of quadrilaterals, which are four-sided polygons. However, they have different properties and characteristics that make them distinct from each other. In this article, we will explore how a rhombus is related to a parallelogram, and what are the similarities and differences between them.
Contents
What is a Rhombus?
A rhombus is a special kind of parallelogram, where all four sides have the same length. This means that a rhombus is also an equilateral quadrilateral. A rhombus has the following properties:
- Opposite sides are parallel and equal in length.
- Opposite angles are equal in measure.
- The diagonals bisect each other at right angles.
- The diagonals also bisect the opposite angles.
- The area of a rhombus is half the product of the diagonals.
- The perimeter of a rhombus is four times the length of one side.
A rhombus can also be called a diamond, because of its shape. However, not all diamonds are rhombi, as some may have different angles. A rhombus can also be seen as a special case of a kite, which is another type of quadrilateral with two pairs of adjacent sides equal in length.
What is a Parallelogram?
A parallelogram is a quadrilateral with two pairs of opposite sides parallel. This means that the opposite sides never intersect, and they have the same slope. A parallelogram has the following properties:
- Opposite sides are parallel and equal in length.
- Opposite angles are equal in measure.
- The diagonals bisect each other.
- The area of a parallelogram is the product of the base and the height.
- The perimeter of a parallelogram is twice the sum of the adjacent sides.
A parallelogram can have different shapes, depending on the angles and the lengths of the sides. Some common examples of parallelograms are rectangles, squares, and rhombi.
How are Rhombi and Parallelograms Related?
As we have seen, a rhombus is a special kind of parallelogram, where all four sides are equal in length. This means that every rhombus is also a parallelogram, but not every parallelogram is a rhombus. For example, a rectangle is a parallelogram with four right angles, but it is not a rhombus unless it is also a square.
Another way to see how a rhombus is related to a parallelogram is to look at their diagonals. In both shapes, the diagonals bisect each other, but in different ways. In a parallelogram, the diagonals bisect each other into two congruent triangles. In a rhombus, the diagonals bisect each other at right angles, forming four congruent right triangles.
We can also compare the formulas for the area and the perimeter of both shapes. In both cases, the area depends on the length of the diagonals, but in different ways. In a parallelogram, the area is equal to the product of one diagonal and its corresponding height. In a rhombus, the area is equal to half the product of both diagonals. Similarly, in both cases, the perimeter depends on the length of one side, but in different ways. In a parallelogram, the perimeter is equal to twice the sum of two adjacent sides. In a rhombus, the perimeter is equal to four times one side.
Conclusion
In conclusion, we can say that a rhombus and a parallelogram are both types of quadrilaterals with two pairs of parallel sides. However, they differ in their angles, their side lengths, and their diagonal properties. A rhombus is a special kind of parallelogram where all four sides are equal in length, and the diagonals are perpendicular and bisect the opposite angles. A parallelogram can have different shapes depending on its angles and side lengths, such as rectangles, squares, or rhombi.
According to BYJU’S, “A rhombus might be considered as the subset of the shape parallelogram.” This means that every property that applies to a parallelogram also applies to a rhombus, but not vice versa. Therefore, we can say that a rhombus is related to a parallelogram by being more specific and restrictive in its definition and characteristics.
