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.
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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