Quadrilaterals: Rhombus and Parallelogram
A quadrilateral is a polygon with four sides. 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.
Rhombus and parallelogram are also considered quadrilaterals as they possess the basic property of quadrilaterals. But are these two shapes different from each other? Let’s find out the difference between a parallelogram and a rhombus in this article.
What is a Rhombus?
Rhombus is a four-sided two-dimensional 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. Rhombus is also called an equilateral quadrilateral, a diamond or a lozenge.
The properties of square and rhombus are similar, but the main distinguishing property is that square has all the angles equal to 90o, and rhombus does not. Also, all rhombus are not squares but all squares are rhombus.
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). They form scalene triangles.
Opposite angles of the rhombus are equal and a diagonal bisects the internal angles.
Adjacent sides are equal in lengths.
Consider the below figure of a rhombus we have,
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Sides AB = BD = DC = CA
Diagonal ADCB
Angle CAB = angle BDC and angle ACD = angle ABD
As diagonal AD and BC bisects the opposite angles, so angle ABC = angle CBD and angle BCD = angle BCA
What is a Parallelogram?
A parallelogram is a four-sided two-dimensional quadrilateral whose opposite sides are parallel and congruent to each other. A parallelogram is also referred to as a slanting rectangle. Opposite interior 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 while parallelogram does not. This means that all rectangles are parallelograms but the vice versa is not true.
Some of the important properties of a parallelogram are:
Opposite sides are of equal length and are parallel to each other.
Diagonals bisect the opposite angles.
Diagonals bisect each other.
Each diagonal bisects the parallelogram in two equal triangles.
Consider the below figure of a parallelogram we have,
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Side AC = side BD and side AB = side CD
Side AB ∥ side CD and side AC ∥ side BD
Angle CAB = CDB and angle ACD = angle ABD
Diagonal AD bisects diagonal BC
Diagonal BC bisects parallelogram in two equal triangles △ABC = △BCD
Diagonal AD bisects parallelogram in two equal triangles △ ACD =△ABD
Difference Between Rhombus and Parallelogram
Rhombus and parallelograms are closely related to each other but they are still different. They are two different quadrilaterals. Some of the key difference between rhombus and parallelogram in the tabular form are:
Rhombus Vs Parallelogram
How to Identify Whether a Quadrilateral is a Rhombus or a Parallelogram?
This is an obvious question every student has in their mind. To identify the nature of a quadrilateral, there are a few things we need to observe and do.
First of all, measure the length of all sides. If the length of all sides are the same, it may be a square or rhombus, but never a parallelogram.
Now check the diagonals if they bisect each other at right angles, and make the conclusion accordingly
Last thing is to check the opposite angles.
Considering all these things, you can conclude your answer with proper justification.
Conclusion
Thus, we conclude that a rhombus is a special kind of parallelogram and that every rhombus can be a parallelogram but not vice versa. This is because in addition to parallel sides, rhombus also has all the sides equal, whereas in parallelogram opposite sides are parallel but adjacent sides size may not be the same.
FAQs on Difference Between Rhombus and Parallelogram
1. 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.
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?
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?
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?
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.
5. How is rhombus different from a square?
Square | Rhombus |
All the angles are equal. | Only the opposite angles are equal to each other. |
Each angle should be 90°. | Angles need not measure 90°. |
Both the diagonals are equal in length. | The diagonals are of unequal length. |
Its sides are perpendicular to each other. | Its sides need not necessarily be perpendicular to each other. |
There are four lines of symmetry. | There are two lines of symmetry. |
It can be inscribed in a circle | It cannot be inscribed in a circle. |
6. Is trapezoid a parallelogram?
No, a trapezoid is not a parallelogram. This is because a 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 are unequal.