Difference Between Rhombus and Parallelogram

Similarities Between Rhombus and Parallelogram

Earlier we have learned what a quadrilateral is. 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. There are different types of quadrilaterals like, square, rectangle, trapezium, kite, rhombus, parallelogram, etc. these shapes are similar to visualize but they differ from each other because of their properties. Here let us discuss what are the similarities between rhombus and parallelogram and let us explain the difference between a parallelogram and a rhombus.

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.

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).

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

  • Adjacent sides are equal in lengths.

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.

Consider the below figure of a rhombus we have,

  • Sides AB = BD = DC = CA

  • Diagonal AD \[\perp\] CB

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

  • Diagonal AD and BC bisects the opposite angles.

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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.

Some of the important properties of a parallelogram are:

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

  • Opposite angles are congruent and the diagonal bisects it.

  • Diagonals bisect each other

  • Each diagonal bisects the parallelogram in two equal triangles.

Consider the below figure of a parallelogram we have,

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

  • Side AB \[\parallel\] side CD and side AC \[\parallel\] side BD

  • Angle CAB = CDB and angle ACD = angle ABD

  • Diagonal AD bisects diagonal BC

  • Diagonal BC bisects parallelogram in two equal triangles \[\triangle\] ABC = \[\triangle\] BCD

  • Diagonal AD bisects parallelogram in two equal triangles \[\triangle\] ACD = \[\triangle\] ABD

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Rhombus Vs Parallelogram

  • As we observe that rhombus and parallelogram there are a lot more similarities between rhombus and parallelogram both are the quadrilaterals having four sides. Both are two-dimensional shapes. 

  • Both rhombus and parallelogram are four-sided quadrilaterals with opposite sides parallel, opposite angles equal, the sum of their interior angles is 3600.

  • But taking into account some of the properties of rhombus and parallelogram we can justify that rhombus and a parallelogram are two different types of quadrilateral. 

  • Rhombus and parallelograms are closely related to each other but they are still different. The main difference between them is rhombus is a quadrilateral with all its four sides equal while parallelogram has its opposite sides equal.

Now let us explain the difference between a parallelogram and a rhombus.

Rhombus and parallelograms are two different quadrilaterals. Some of the key difference between rhombus and parallelogram are:

Difference Between Rhombus and Parallelogram

Sr.No

Rhombus

Parallelogram

1

Rhombus is a flat two-dimensional figure, where all its four sides are parallel to each other

A parallelogram is a flat- two-dimensional figure, whose only opposite sides are parallel to each other

2

All the four sides are of equal lengths

Opposite sides are of equal lengths

3

Area of Rhombus is Area =  d1d2/2, where d1 and d2 are diagonals.

The area of a parallelogram is Area = bh, where b and h are base and height.

4

The perimeter of a rhombus is given by P = 4a, where “a” is the side

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

5

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

Diagonals bisect each other, forming congruent triangles


6

Every rhombus will be a parallelogram

Every parallelogram will not be 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 language word “parallelogrammon” with the meaning “parallel lines”.


Solved Examples

1. Identify the Below Figure is a Rhombus or a Parallelogram

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Solution: In Quadrilateral above

  • All of its sides are equal

  • Opposite sides are parallel

  • Diagonal bisects at right angles

  • Opposite angles are equal

From all these properties we can conclude that the quadrilateral is a rhombus.

FAQ (Frequently Asked Questions)

1. What is Rhombus?

Answer: 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.

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2. What is Parallelogram?

Answer: 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.

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3. Is a Square a Rhombus?

Answer:

  •  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?

Answer: 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.