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Rotational Symmetry

Symmetry is defined for objects or shapes which are exactly identical to each other when placed one over the other. Rotational symmetry is exhibited by different geometrical shapes such as circles, squares, rhombus, etc. We will be studying more about rotational symmetry, its order, and the angle of rotation in this article.

1. Rotational Symmetry Definition
2. Order of Rotational Symmetry
3. FAQs on Rotational Symmetry

Rotational Symmetry Definition

An object when rotated in a particular direction, around a point is exactly similar to the original object is known to have rotational symmetry. When a geometrical shape is turned, and the shape is identical to the origin, it is known to exhibit rotational symmetry. is also known as radial symmetry. Geometrical shapes such as squares, rhombus, circles, etc. show rotational symmetry. We also see rotational symmetry existing in daily life such as exhaust fans, windmills, etc.

Below is an example of rotational symmetry shown by a starfish. If the starfish is turned around point P, it looks similar from all directions.

Order of Rotational Symmetry

The order of rotational symmetry is defined as the number of times the geometrical figure is identical to the original figure undergoing one complete rotation. The number of times the rotated figure exactly fits into the original figure gives the order of rotational symmetry.

The angle of rotational symmetry is defined as the smallest angle at which the figure can be rotated to coincide with itself and the order of symmetry is how the object coincides with itself when it is in rotation. Let’s look into some examples of rotational symmetry as shown below.

From the above images of a rhombus, we observe that it fits onto itself twice in one full rotation of 360°. Therefore, we can conclude that the order of rotational symmetry in a rhombus is 2 and the angle of rotation is 180°.

A square is a quadrilateral with all its internal angles measuring 90° each. From the above figure we see that the order of rotational symmetry of a square is 4 as it fits into itself 4 times in a complete 360° rotation. The angle of rotation is 90°.

Related Articles on Rotational Symmetry

Check the following links related to rotational symmetry.

Rotational Symmetry Examples

  1. Example 1: What are the angles at which a square has rotational symmetry?

    Solution:

    Rotational symmetry is defined as a type of symmetry in which the image of a given shape is exactly identical to the original shape or image in a complete turn or a full angle rotation or 360° rotation. It exists when a shape is turned, and the shape is identical to the original. Hence, a square has a rotational symmetry at an angle of 90° and the order of rotational symmetry is 4.

  2. Example 2: Show the rotational symmetry of an equilateral triangle.

    Solution:

    An equilateral triangle has 3 sides of equal measure and each internal angle measuring 60° each.

    From the above figure, we see that the equilateral triangle exactly fits into itself 3 times at every angle of 120°. Thus, the order of rotational symmetry of an equilateral triangle is 3 and its angle of rotation is 120°.

  3. Example 3: What is the order of rotational symmetry of a circle? Explain.

    Solution:

    A circle will follow rotational symmetry at every angle or alignment irrespective of how many ever times it is rotated throughout. This is true because a circle looks identical at any angle of rotation. Therefore, we can say that the order of rotational symmetry of a circle is infinite.

Practice Questions on Rotational Symmetry

FAQs on Rotational Symmetry

What is Rotational Symmetry?

Rotational symmetry is a type of symmetry that is defined as the number of times an object is exactly identical to the original object in a complete 360° rotation. It exists in different geometrical objects such as rhombus, squares, etc.

How to find Order of Rotational Symmetry?

The order of rotational symmetry can be easily found by counting the number of times an object fits into itself in one complete rotation of 360°. For example, the order of rotational symmetry of a rhombus is 2.

What is the Order of Rotational Symmetry of an Equilateral Triangle?

The order of rotational symmetry of an equilateral triangle is 3 as it fits 3 times into itself in a complete turn of 360°.

What is the Smallest Angle of Rotational Symmetry for a Square?

The smallest angle of rotational symmetry for a square is equal to 90° as in every 90° rotation, the figure exactly fits into the original one.

What is the Rotational Symmetry of a Pentagon?

A regular pentagon has 5 sides of equal length. The order of rotational symmetry of a regular pentagon is 5 as it coincides 5 times with itself in a complete revolution.

What is Rotational Symmetry of Order 2?

The rotational symmetry of order 2 signifies that a figure is identical and fits into itself exactly twice in a complete rotation of 360°.

What is the Order of Rotational Symmetry for a Rhombus?

The order of rotational symmetry of a rhombus is 2 as it fits 2 times into itself in a complete turn.

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