Rotational Symmetry

What is rotational symmetry?

When the figure is turned about a fixed point; it is called rotation.

The shapes and objects that look the same after a certain amount of rotation are said to have rotational symmetry. Some shapes look the same after half a turn. If we turn English alphabet S around a centre point by 180° we get the alphabet S in the same position. The angle of turning during a rotation is called the angle of rotation. A complete turn means 360°, so a half turn means 180° and a quarter turn means 90°.

This rotation can be: (a) clockwise (b) anticlockwise

The fixed about which the figure is rotated is called centre of rotation.

The angle of turning during rotation is called the angle of rotation.

A quarter turn means a rotation of 90°

A half turn means a rotation of 180°

A full turn means a rotation of 360°

A figure is said to have rotational symmetry if it onto more than once during a complete rotation, i.e., 360°

Take a square piece and draw lines, as shown in the figure. Place a pin in the centre where the lines meet. Now, rotate this square by 90° about its centre. The square looks exactly the same. In a full turn 360° there are 4 positions when the square looks exactly the same.

Rotational Symmetry

Thus, a square has a rotational symmetry of order 4 about its centre of rotation. Hence, the angle of rotation is 90°.

Order of rotational symmetry = \(\frac{360}{\textrm{Angle of Rotation}}\)

A figure has a rotational symmetry of order 1, if it can come to its original position after full rotation or 360°.

● Related Concepts

Linear Symmetry

Lines of Symmetry

Point Symmetry

Order of Rotational Symmetry

Types of Symmetry

Reflection

Reflection of a Point in x-axis

Reflection of a Point in y-axis

Reflection of a point in origin

Rotation

90 Degree Clockwise Rotation

90 Degree Anticlockwise Rotation

180 Degree Rotation





7th Grade Math Problems

8th Grade Math Practice

From Rotational Symmetry to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Adding 5-digit Numbers with Regrouping | 5-digit Addition |Addition

    Mar 18, 24 02:31 PM

    Adding 5-digit Numbers with Regrouping
    We will learn adding 5-digit numbers with regrouping. We have learnt the addition of 4-digit numbers with regrouping and now in the same way we will do addition of 5-digit numbers with regrouping. We…

    Read More

  2. Adding 4-digit Numbers with Regrouping | 4-digit Addition |Addition

    Mar 18, 24 12:19 PM

    Adding 4-digit Numbers with Regrouping
    We will learn adding 4-digit numbers with regrouping. Addition of 4-digit numbers can be done in the same way as we do addition of smaller numbers. We first arrange the numbers one below the other in…

    Read More

  3. Worksheet on Adding 4-digit Numbers without Regrouping | Answers |Math

    Mar 16, 24 05:02 PM

    Missing Digits in Addition
    In worksheet on adding 4-digit numbers without regrouping we will solve the addition of 4-digit numbers without regrouping or without carrying, 4-digit vertical addition, arrange in columns and add an…

    Read More

  4. Adding 4-digit Numbers without Regrouping | 4-digit Addition |Addition

    Mar 15, 24 04:52 PM

    Adding 4-digit Numbers without Regrouping
    We will learn adding 4-digit numbers without regrouping. We first arrange the numbers one below the other in place value columns and then add the digits under each column as shown in the following exa…

    Read More

  5. Addition of Three 3-Digit Numbers | With and With out Regrouping |Math

    Mar 15, 24 04:33 PM

    Addition of Three 3-Digit Numbers Without Regrouping
    Without regrouping: Adding three 3-digit numbers is same as adding two 3-digit numbers.

    Read More