When one rotation is completed, the rotating object comes back to the position where it started. During a complete rotation, the object moves through 360°.

**Rotational
Symmetry**

We have already learnt about rotation. **Rotation**
means turning around a centre. The paper windmill, merry-go-round, fan, tops, wheels
of vehicles, fidget spinner are few examples of rotating objects that we see in
our life.

When one rotation is completed, the rotating object
comes back to the position where it started. During a complete rotation, the object
moves through 360°.

** **

**Think about the situation**

1) Take two rectangular biscuits from the same packet
and put one on the other. Holding one biscuit firmly rotate the other on it about
the centre.

How many times does it fit exactly on the other
in a complete rotation? Two times.

2)
In the example given below, if you rotate the fidget
spinner about the centre, there are three positions in which the fidget spinner
matches exactly the same in a full rotation.

3) Place a set square
(containing angles 60°, 30° and 90°) on a paper and draw an outer line around it.
What type of triangle do you get? Yes, Scalene triangle. If you rotate it about
the centre, there is only one position in which the set square fits exactly inside
the outer line.

In the above situations 1 and 2, the total number
of times the rectangular biscuit and the fidget spinner matches exactly with itself
in one complete rotation is 2 and 3. This is called the ** order of rotational symmetry.** In situation
3, the set square matches itself only once in one complete rotation and hence has
no rotational symmetry.

An object is said to have a ** rotational symmetry** if it looks the same after
being rotated about its centre through an angle less than 360° (If the order of
rotation of an object is atleast two).

**Think**

Can you identify the object which does
not have rotational symmetry in the above situations? Why?

** **

__Example 10__

A man-hole
cover of a water sump is in square shape.

i) In how many ways we can fix that to close the
sump?

ii) What is its order of rotational symmetry?

**Solution**

i) We can fix it in 4 ways as shown above.

ii) The order of rotational symmetry is 4.

** **

**Think**

**Suppose, the man hole cover of the water sump is in circular shape.**

**i) The number of ways to close that circular lid is _{——————}**

**ii) What is its order of rotational symmetry?**

**Activity**

Find the order of rotational symmetry
by fixing the relevant shape in different ways.

** **

__Example 11____ __

Find the order of rotation for the following figures.

**Solution**

** **

__Example 12__

Find the order of rotation for the following shapes.

**Solution**

** **

__Example 13____ __

Join six identical squares so that atleast one side of a square fits exactly with any other square and have rotational symmetry (any three ways).

**Solution**

The opening in the given spanner has
six sides, so it is a hexagon. The spanner has rotational symmetry of order 6 and
fits a hexagonal bolt in any of six positions.

Tags : Symmetry | Term 3 Chapter 4 | 6th Maths , 6th Maths : Term 3 Unit 4 : Symmetry

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6th Maths : Term 3 Unit 4 : Symmetry : Rotational Symmetry | Symmetry | Term 3 Chapter 4 | 6th Maths

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