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Rhombus is a type of parallelogram whose all sides and its length are equal with each other. It consists of two lines of symmetry. The line symmetry here means the division of rhombus into two identical halves. It is a closed figure having a 2D plane. It is also known as a special type of parallelogram that has some special properties.
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Keyterms: Rhombus, symmetry, angles, right angles, interior angles, quadrilateral
Rhombus Definition
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Rhombus can be defined as a geometrical shape and a special type of parallelogram whose all sides are equal to each other. Rhombus can be called a square when all the angles of a Rhombus are at right angles.
Rhombus
Some of the properties of a Rhombus are:
- All of its sides are equal with each other.
- Both the diagonals of a rhombus can bisect with each other at right angles or 90°.
- The opposite sides are in parallel with each other and its opposite angles are also equal.
- The sum of the adjacent angles of a square is equal to 180°.
- There are a total of four interior angles present in a rhombus.
- Sum of interior angles of a rhombus is 360 degrees just as in any quadrilateral.
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Difference between Rhombus and Square
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Rhombus has equal sides and it is also called an equilateral quadrilateral. Although both rhombus and square have all of its sides in equal length, there is a slight difference between a rhombus and a square.
| Rhombus | Square |
|---|---|
| Rhombus is a type of quadrilateral. | Square is also a type of quadrilateral. |
| All the sides are of the same length. | All the four sides are equal in square. |
| In rhombus, opposite sides are parallel to each other. | The opposite sides are parallel to each other. |
| The opposite angles are equal to 90°. | All the interior angles measure to 90°. |
| The length of the diagonals are different when measured. | The length of the diagonals are same or equal when measured. |
| Rhombus has only two symmetry lines. | Whereas in the square, there are four lines of symmetry. |
| Area of a rhombus = ½ diagonal 1 * diagonal 2 | Area of a square: Side × Side or Side² |
Area of Rhombus
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Rhombus is a type of quadrilateral. It bisects its diagonal in equal parts. Its diagonal intersects at 90°. A rhombus is nothing but the sum of two congruent triangles. The area of the rhombus can be found by three methods.
First by multiplying its diagonal with ½.
A = 1/2 d1 * d2
Where, d1 and d2 are its two diagonals.
Second, find its area by its base and height by multiplying its base and height.
A= base * height
And lastly, by using trigonometry, the area can be found.
A = side2 *(sinA)
Lines of Symmetry in Rhombus
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Rhombus line of symmetry is defined as an imaginary line through which a rhombus can be folded into two equal halves so that each one of them is symmetrical in nature. In other words, the lines of symmetry, are the lines that divide it into two equal halves and each half is the mirror image of the other. A rhombus has two lines of symmetry. Different objects have a different number of symmetrical lines.
Lines of Symmetry in Rhombus
There are two lines of symmetry which cuts it into two identical parts. If the folded part of the rhombus can be exactly superimposed with each other with all of its edges and the corners coinciding, then the line that is folded represents the line of symmetry and the shape is symmetrical. The shape of the rhombus is symmetrical either through its length, width or its diagonal. Both the lines of symmetry in a rhombus are from its diagonal. Therefore, it can be said the rhombus lines of symmetry are both its diagonals.
Things to Remember
- Rhombus can be defined as a two-dimensional closed plane figure.
- Symmetry here means the "mirror image”. The object when turned or flipped back and it appears the same, it is called the symmetry of an object.
- When a line divides an object into the two equal halves, then it is called the lines of symmetry.
- Lines of Symmetry are imaginary lines in the rhombus through which it appears like it is folded into two equal halves making it symmetrical.
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Sample Questions
Ques. What is a rhombus? (2 marks)
Ans. The rhombus is defined as a closed 2D plane figure. It has four sides of equal length. The rhombus looks like a diamond. It can be considered as a type of parallelogram. It has different unique properties.The rhombus is an equilateral quadrilateral which means the sides of it are equal in length.
Ques. What are the properties of a rhombus? (2 marks)
Ans. There are different properties of a rhombus which makes it a unique quadrilateral.
- The length of all the sides are equal with each other.
- The opposite sides are parallel to each other.
- The opposite angles when measured are equal or same.
- The diagonals of a rhombus bisect with each other at right angles.
- The diagonals are known as the perpendicular bisectors of each other.
Ques. Define the line of symmetry in a rhombus? (2 marks)
Ans. The rhombus is a closed figure having all the sides equal in length. It consists of two symmetry lines in it. The lines are imaginary lines through which it can be folded into two equal halves to make them symmetrical. This property is known as the rhombus line of symmetry. In this figure, there are two diagonals of a rhombus that bisects each other. Hence, the diagonals seem like when folded or tilted then the rhombus appears in the two similar halves.
Ques. Write in brief about the lines of symmetry in a non-square rhombus? (2 marks)
Ans. The square is one particular type of rhombus. The interior angles measure 90° in the rhombus. The rhombus is very different from a square. The angles of a rhombus are not 90°. In Rhombus, the number of lines of symmetry is 4. Here, the lines of symmetry are made through its diagonals. Rhombus, the lines of symmetry are drawn through its vertical axis and horizontal axis.
Ques. How Many Lines of Symmetry are present in a Rhombus? (2 marks)
Ans. A rhombus has 2 lines of symmetry. The symmetry lines in the rhombus are its diagonals. There are two diagonals in a rhombus that are bisected with each other.
It makes the right angle of 90°.
Ques. Does a Rhombus Have Rotational Symmetry? (2 marks)
Ans. The question has an answer of yes. The rhombus is a type of parallelogram having two opposite sides parallel. It has rotational symmetry. It has the rotational symmetry of 180° in the figure.
Ques. What is the area of a rhombus? (2 marks)
Ans. There are different ways to find out the area of the rhombus.
- Area of a Rhombus = base × height sq. units
- Area of a rhombus = A = 1/2 d1 * d2
- Area of a Rhombus = side2 × sin(A) sq. units.
Ques. What is the difference between the square and rhombus? (2 marks)
Ans. The difference between the square and rhombus is given below.
Basically square and the rhombus have all four sides equal in length. But a square has 90° of all the angles whereas when measured in a rhombus, only the opposite angles are equal.
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