**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"

Apart from the stuff given above, if you want to know more about "Order of rotational symmetry", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**