Rhombus Line of Symmetry

What does the Line of Symmetry in Rhombus Means?

A rhombus has two lines of symmetry i.e horizontal line of symmetry and vertical line of symmetry. In a  rhombus, the line of symmetry divides it into two equal halves and each half of the rhombus is considered as the mirror image of the other. The lines of symmetry of rhombus are drawn from its diagonals. Due to this, it is said that rhombus lines of symmetry are its both diagonals. Different objects have different numbers of lines of symmetry. In this article, we will discuss what is symmetry, what is the line of symmetry, what does the line of symmetry in rhombus means, rotational symmetry of rhombus, How do rhombus lines of symmetry differ from the line of symmetry of squares etc.

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What is Known as Symmetry?

The definition of the symmetry states that “ symmetry is a mirror image”.  Any object or shape looks similar to the original after it has been turned or flipped, then it is known as symmetry. Symmetry basically exists in patterns. The word symmetry is often heard in day-to-day life as it is found all around us i,.e, in nature, art and architecture etc. It is a balanced and proportional resemblance that can be seen in two i.e one half of a shape is the mirror image of the other half. Any shape which is not symmetry is asymmetrical in shape.

What is Known as the Line of Symmetry?

Any line dividing an object into two halves such that its two parts are identical is known as lines of symmetry. These parts are also said to be symmetrical to each other.


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For example, the images given above exhibit a line of symmetry which is dividing the red outlined shape into two halves that are exactly similar.

From the above example, we can see the following observations:

The sides of the image divided up by the lines of symmetry must look similar.

If the page is folded( on which image is formed) sling the line of symmetry, every part of the image will completely overlap the other part.

These observations help us to examine the line of symmetry in any shape.

Line of Symmetry Examples

Some of the lines of symmetry examples are given below:

  • A triangle has 3, 1 or even no lines of symmetry

  • A rhombus has 2 lines of symmetry

  • An equilateral triangle has three lines of symmetry.

  • A regular pentagon has 5 lines of symmetry

  • A regular heptagon has 7 lines of symmetry.

Line of Symmetry in Rhombus

A rhombus has two lines of symmetry i.e horizontal line of symmetry and vertical line of symmetry. Both lines of symmetry of rhombus divide it into two equal halves. The lines of symmetry of rhombus are drawn from its diagonals. Due to this, it is said that rhombus lines of symmetry are the both diagonals of rhombus.


How Do Rhombus Lines of Symmetry Differ From The Line of Symmetry of Squares?

Both square and rhombus are two-dimensional geometric figures whose all the four sides are equal in length along with the opposite side parallel to each other. Though rhombus and square have many similarities but there are some differences between them. These are:

  • All the angles of a square are 90 degrees i.e right angle formed at each vertex whereas opposite sides of a Rhombus are of equal measures.

  • Due to the difference in the angle measurement of square and rhombus, both have different lines of symmetry.

  • A rhombus has two lines of symmetry whereas a square has 4 lines of symmetry.

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Rotational Symmetry of Rhombus.

The rotational symmetry defines that when an object is rotated on its own axis, its shape appears the same as the original shape. 

A rhombus is a 2-dimensional geometrical figure whose all the four sides are of equal length.In contrast with square, the measurement of all the four angles of a rhombus  is not equal to 90 degrees. A rhombus has 2 lines of symmetry i.e. the vertical line of symmetry and the horizontal line of symmetry. The angle of rotation for the rhombus is 180 degrees whereas the order of rotational symmetry of rhombus is 2.

Solved Examples

  1. Is the dotted line given on the shape below represents a line of symmetry.


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The shape given above can be imagined as paper and if we fold a paper through the dotted line, transparently the shapes of both the sides of the line don't get matched.

So, ther dotted line on the given shape is not a line of symmetry.


  1. Which of the following figures does not have a line of symmetry?


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Solution:

If we fold both the papers A and B from top to down as shown in figure A1 and B1, we will get  a line of symmetry in figure A but not in figure B. If we fold  both the papers from left to right as given  in figure A2 and B2 below, we will get any line of symmetries in both the figures A and B.


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Quiz Time

  1. A Rhombus is Symmetrical About

  1. Each of its diagonals

  2. The perpendicular bisector of each of its sides

  3. The line joining the midpoint of its opposite side.

  4. None of these


      2. How Many Lines of Symmetry Does Rhombus Have?

  1. 1

  2. 2

  3. 3

  4. 4

Facts

  • The line of symmetry is also known as the axis of symmetry or mirror line

  • A circle includes infinite lines of symmetry

FAQ (Frequently Asked Questions)

1. Define rhombus and state its properties.

A rhombus is a type of parallelogram with all its sides equal in length. The shape of a rhombus looks like a diamond.


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Properties of Rhombus


  1. All sides of a rhombus are equal in length

  2. The opposite sides of a rhombus are parallel.

  3. The opposite angles of a  rhombus are equal.

  4. The diagonals of a rhombus bisect the angles

  5. The diagonals of a rhombus are considered as the perpendicular bisectors of each other.

2. Does rhombus have rotational symmetry?

Any object or shape when rotated on its own axis and still it appears the same after the rotation, then it is said to have rotational symmetry. Many geometrical shapes appear to be symmetry when they are rotated 90°,180°, 360°, clockwise or anticlockwise directions. Some of the examples are hexagon, square, rhombus etc.

Yes, rhombus has rotational symmetry of 180 degrees, and the order of rotational symmetry of rhombus is 2. The order of rotational memory of rhombus states that it appears similar to its original shape after it has been rotated twice.