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.

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. 

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

Example 2 : 

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

Solution :

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. 

So, a square has rotational symmetry of order 4.

Example 3 : 

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

Solution :

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. 

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

Example 4 : 

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

Solution :

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. 

So, a parallelogram has rotational symmetry of order 2.

Example 5 : 

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

Solution :

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. 

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

Example 6 : 

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

Solution :

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. 

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

Example 7 : 

What is the order of rotational symmetry of a trapezium ?

Solution :

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. 

So, a trapezium has rotational symmetry of order 1.

Example 8 : 

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

Solution :

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. 

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

Example 9 : 

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

Solution :

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

So, a kite has rotational symmetry of order 1.

Example 10 : 

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

Solution :

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

So, a rhombus has rotational symmetry of order 2.

Example 11 : 

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

Solution :

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

So, an ellipse has rotational symmetry of order 2.

Example 12 : 

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

Solution :

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.

So, a circle has infinite order of rotational symmetry. 

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