Rhombus Line of Symmetry

A rhombus is a closed two-dimensional plane figure. It is considered a special type of parallelogram, and due to its unique properties, it gets an individual identity as a quadrilateral. It is an equilateral quadrilateral since all the sides of the rhombus are equal in length. The term ‘rhombus’ has been derived from the ancient Greek word ‘rhómbos', which means something that spins.

What is Known as Symmetry?

The definition of the symmetry states that “symmetry is a mirror image”. If 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 symmetrical 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 a line 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) slinging 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.

Lines of Symmetry in Rhombus

In a rhombus, there are two lines of symmetry. These are imaginary lines through which the rhombus is folded into two halves, making it symmetrical, known as rhombus lines of symmetry. If the folded part exactly lies on the other half and all the edges and corners coincide with each other, then the folded line represents a line of symmetry and that shape is symmetrical along its length, width, or diagonals. The diagonals are the two lines of symmetry in a rhombus. This is because when the rhombus is folded along the diagonal line, it gets the same shape as two halves. 

Lines of Rotational Symmetry in a Rhombus

A rhombus has rotational symmetry of order two. Rotational symmetry is a type of symmetry in which the image or the rotated shape looks exactly similar to the original shape on all sides. So, when a shape is turned about a complete rotation and the shape is identical to the original shape, it proves that rotational symmetry exists.

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 ,there are some differences between them. These are:

• All the angles of a square are 90 degrees, i.e., right angles, formed at each vertex, whereas opposite sides of a rhombus are of equal measure.

• 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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Lines of Symmetry in a Non-square Rhombus

A square is a special kind of rhombus with each of its internal angles measuring 90°. A non-square rhombus is completely different from a square when considering its internal angles. The internal angles of a non-square rhombus are not equal to 90°, like a square rhombus. In a non-square rhombus, the number of lines of symmetry is 2, whereas in the square, the number of lines of symmetry is 4. The lines of symmetry in a non-square rhombus are drawn through its diagonals, whereas the lines of symmetry in a square are drawn through its vertical axis, horizontal axis, and two diagonals.

Rotational Symmetry of a Rhombus:

The rotational symmetry states 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 to 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 the rhombus is 2.

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 a 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.
  
  

Solved Examples

1. Does 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.

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

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If we fold both the papers A and B from top to down as shown in figures 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 figures A2 and B2 below, we will get any line of symmetries in both the figures A and B.