**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.

**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.

**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.

Hence, 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.

Hence, 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.

Hence, 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.

Hence, 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.

Hence, 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.

Hence, 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.

Hence, 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.

Hence, 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.

Hence, 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.

Hence, 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.

Hence, a circle has infinite order of rotational symmetry.

After having gone through the stuff, we hope that the students would have understood "Order of rotational-symmetry"

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