Maths

Difference between Rhombus and Parallelogram in tabular form

There are many different varieties of quadrilaterals in geometry, such as the parallelogram, rhombus, square, rectangle, trapezoid, and kite, all of which have similar characteristics, making it difficult for people to understand them. An inclined square with equal neighboring sides is referred to as a rhombus. A parallelogram, on the other hand, is a slanted rectangle with two sets of parallel opposite sides.

The fundamental difference between a rhombus and a parallelogram is that a rhombus has all of its sides the same length, but a parallelogram is a rectilinear figure with opposite sides that are parallel.

Rhombus Definition

A rhombus is a quadrilateral with equal side lengths. It has four sides that are parallel to each other and is flat in shape.

A rhombus’s opposite angles are equal, that is, they are of the same degree. Its diagonals meet at 90 degrees (right angles), forming two equilateral triangles that are perpendicular to each other. It has extra sides, which implies that the sum of their measurements equals 180 degrees. An equilateral parallelogram is another name for it.

Parallelograom Definition

A parallelogram is a flat, four-sided figure with opposite sides that are parallel and congruent, as the name implies.
The lengths of its opposing angles are equal, and the lengths of its subsequent angles are additional, meaning that the sum of their lengths equals 180 degrees. It has two congruent triangles formed by its diagonals bisecting each other.

Rhombus Vs Parallelogram: Comparison table

Rhombus

 

Parallelogram

 

Rhombus refers to a four-sided flat-shaped figure with all sides congruent.

 

A parallelogram is a four-sided plane figure whose opposite sides are parallel to each other.
All four sides are the same length.

 

The opposite sides have the same length.
The diagonals bisect each other at right angles to form a scalene triangle.

 

The diagonals bisect to form two congruent triangles.
The area of the Rhombus is xy/2, where x and y are diagonals.The area of the parallelogram is ah, where a and h are base and height.
Its perimeter is given by p = 4x, where “x” is a side.

 

The perimeter of a parallelogram is given by, X = 2(a+b), where “a” is the side and “b” is the base.
Diagonals of a rhombus bisect each other at right angles and form a scalene triangle.

 

Diagonals of a parallelogram bisect each other and form congruent triangles.

Key Differences between Rhombus and Parallelogram

On the following reasons, the distinction between rhombus and parallelogram can be clearly drawn:

  • A rhombus is a four-sided quadrilateral of flat shape with congruent lengths on all sides. A parallelogram is a four-sided plane shape with opposing sides that are parallel.
  • Only the opposite sides of a parallelogram are equal, but all sides of a rhombus are the same length.
  • Two scalene triangles are formed when the diagonals of a rhombus are bisected at right angles. Unlike a parallelogram, which has two congruent triangles formed by the diagonals bisecting one other.
  • The area of a rhombus is calculated using the formula (pq) / 2, where p and q are the diagonals. The area of a parallelogram, on the other hand, may be computed by multiplying the base and height.
  • The following formula can be used to calculate the perimeter of a rhombus: 4a, where an is the rhombus’s side. The perimeter of a parallelogram, on the other hand, may be computed by adding the base and height and multiplying the result by two.

Conclusion:

Both the parallelogram and the rhombus are quadrilaterals with parallel opposite sides, equal opposed angles, and a 360-degree total of internal angles.

A rhombus is a form of the parallelogram in its own right. As a result, each rhombus can be considered a parallelogram, but not the other way around.

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