ORDER OF ROTATIONAL SYMMETRY OF A SQUARE

About "Order of rotational symmetry of a square"

The order of rotational symmetry of a square is, how many times a square fits  on to itself during a full rotation of 360 degrees.

Please look at the images of the square in the order A, B, C, D and E. A is the original image. The images B, C, D and E are generated by rotating the original image A. 

When we look at the above images of square, it fits on to itself 4 times during a full rotation of 360 degrees. 

Hence, order of rotational symmetry of a square is 4  

Order of Rotational symmetry -  Definition

The order of rotational symmetry is that an object has the number of times that it fits on to itself during a full rotation of 360 degrees.

Order of rotational symmetry - Some other Examples 

To have better understanding on "order of rotational symmetry", let us look at some examples. 

Example 1 : 

What is the order of rotational-symmetry of an equilateral triangle ?

Solution :

As explained in the definition, we have to check, how many times an equilateral triangle fits on to itself during a full rotation of 360 degrees. 

Please look at the images of the equilateral triangle in the order A,B and C. A is the original image. The images B and C are generated by rotating the original image A. 

When we look at the above images of equilateral triangle, it fits on to itself 3 times during a full rotation of 360 degrees. 

Hence, an equilateral triangle has rotational symmetry of order 3. 

On this web page "Order of rotational symmetry of a square", next we can look at the order of rotational symmetry of a different figure. 

Example 2 : 

What is the order of rotational-symmetry of a regular pentagon ?

Solution :

As explained in the definition, we have to check, how many times a regular pentagon fits on to itself during a full rotation of 360 degrees. 

Please look at the images of the regular pentagon in the order A, B, C, D, E and F. A is the original image. The images B, C, D, E and F are generated by rotating the original image A. 

When we look at the above images of regular pentagon, it fits on to itself 5 times during a full rotation of 360 degrees. 

Hence, a regular pentagon has rotational symmetry of order 5.

On this web page "Order of rotational symmetry of a square", next we can look at the order of rotational symmetry of a different figure. 

Example 3 : 

What is the order of rotational-symmetry of a parallelogram ?

Solution :

As explained in the definition, we have to check, how many times a parallelogram fits on to itself during a full rotation of 360 degrees. 

Please look at the images of the parallelogram in the order A, B and  C. A is the original image. The images B and C are generated by rotating the original image A. 

When we look at the above images of parallelogram, it fits on to itself 2 times during a full rotation of 360 degrees. 

Hence, a parallelogram has rotational symmetry of order 2.

On this web page "Order of rotational symmetry of a square", next we can look at the order of rotational symmetry of a different figure. 

Example 4 : 

What is the order of rotational-symmetry of an isosceles triangle ?

Solution :

As explained in the definition, we have to check, how many times an isosceles triangle fits on to itself during a full rotation of 360 degrees. 

Please look at the images of the isosceles triangle in the order A and B. A is the original image. The image B is generated by rotating the original image A. 

When we look at the above images of isosceles triangle, it fits on to itself 1 time during a full rotation of 360 degrees. 

Hence, an isosceles triangle has rotational symmetry of order 1. 

On this web page "Order of rotational symmetry of a square", next we can look at the order of rotational symmetry of a different figure. 

Example 5 : 

What is the order of rotational-symmetry of an scalene triangle ?

Solution :

As explained in the definition, we have to check, how many times an scalene triangle fits on to itself during a full rotation of 360 degrees. 

Please look at the images of the scalene triangle in the order A and B. A is the original image. The image B is generated by rotating the original image A. 

When we look at the above images of isosceles triangle, it fits on to itself 1 time during a full rotation of 360 degrees. 

Hence, a scalene triangle has rotational symmetry of order 1.

On this web page "Order of rotational symmetry of a square", next we can look at the order of rotational symmetry of a different figure. 

Example 6 : 

What is the order of rotational-symmetry of a trapezium ?

Solution :

As explained in the definition, we have to check, how many times an trapezium fits on to itself during a full rotation of 360 degrees. 

Please look at the images of the trapezium in the order A and B. A is the original image. The image B is generated by rotating the original image A. 

When we look at the above images of trapezium, it fits on to itself 1 time during a full rotation of 360 degrees. 

Hence, a trapezium has rotational symmetry of order 1.

On this web page "Order of rotational symmetry of a square", next we can look at the order of rotational symmetry of a different figure. 

Example 7 : 

What is the order of rotational-symmetry of a isosceles trapezium ?

Solution :

As explained in the definition, we have to check, how many times an isosceles trapezium fits on to itself during a full rotation of 360 degrees. 

Please look at the images of the isosceles trapezium in the order A and B. A is the original image. The image B is generated by rotating the original image A. 

When we look at the above images of isosceles trapezium, it fits on to itself 1 time during a full rotation of 360 degrees. 

Hence, an isosceles  trapezium has rotational symmetry of order 1.

On this web page "Order of rotational symmetry of a square", next we can look at the order of rotational symmetry of a different figure. 

Example 8 : 

What is the order of rotational-symmetry of a kite ?

Solution :

As explained in the definition, we have to check, how many times a kite fits on to itself during a full rotation of 360 degrees. 

Please look at the images of the kite the order A and B. A is the original image. The image B is generated by rotating the original image A. 

When we look at the above images of kite, it fits on to itself 1 time during a full rotation of 360 degrees. 

Hence, a kite has rotational symmetry of order 1.

On this web page "Order of rotational symmetry of a square", next we can look at the order of rotational symmetry of a different figure. 

Example 9 : 

What is the order of rotational-symmetry of a rhombus ?

Solution :

As explained in the definition, we have to check, how many times a rhombus fits on to itself during a full rotation of 360 degrees. 

Please look at the images of the rhombus the order A, B and C. A is the original image. The images B and C are generated by rotating the original image A. 

When we look at the above images of rhombus, it fits on to itself 2 time during a full rotation of 360 degrees. 

Hence, a rhombus has rotational symmetry of order 2.

On this web page "Order of rotational symmetry of a square", next we can look at the order of rotational symmetry of a different figure. 

Example 10 : 

What is the order of rotational-symmetry of an ellipse ?

Solution :

As explained in the definition, we have to check, how many times an ellipse fits on to itself during a full rotation of 360 degrees. 

Please look at the images of the ellipse the order A, B and C. A is the original image. The images B and C are generated by rotating the original image A. 

When we look at the above images of ellipse, it fits on to itself 2 time during a full rotation of 360 degrees. 

Hence, an ellipse has rotational symmetry of order 2.

On this web page "Order of rotational symmetry of a square", next we can look at the order of rotational symmetry of a different figure. 

Example 11 : 

What is the order of rotational-symmetry of a circle ?

Solution :

As explained in the definition, we have to check, how many times a circle fits on to itself during a full rotation of 360 degrees. 

A circle has an infinite 'order of rotational symmetry'. In simplistic terms, a circle will always fit into its original outline, regardless of how many times it is rotated.

Hence, a circle has infinite order of rotational symmetry. 

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