krit.club logo

Symmetry - Rotational Symmetry

Grade 6CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

Rotational symmetry occurs when an object is rotated around a fixed point and looks exactly like its original position at certain angles before completing a full 360∘360^\circ turn.

•

The fixed point about which the rotation takes place is called the Center of Rotation.

•

The minimum angle by which a shape must be rotated to look identical to the original is called the Angle of Rotation.

•

Common rotation angles include a quarter turn (90∘90^\circ), a half turn (180∘180^\circ), and a full turn (360∘360^\circ).

•

The number of times a figure fits onto itself in one complete rotation of 360∘360^\circ is called the Order of Rotational Symmetry.

•

Every object has rotational symmetry of order 11, as it will always look the same after a full 360∘360^\circ turn. However, a figure is said to have rotational symmetry only if its order is greater than 11.

•

For a regular polygon with nn sides, the order of rotational symmetry is equal to nn.

📐Formulae

Order of Rotational Symmetry=360∘Angle of Rotation\text{Order of Rotational Symmetry} = \frac{360^\circ}{\text{Angle of Rotation}}

Angle of Rotation=360∘n (where n is the order of rotational symmetry)\text{Angle of Rotation} = \frac{360^\circ}{n} \text{ (where } n \text{ is the order of rotational symmetry)}

💡Examples

Problem 1:

Find the order of rotational symmetry and the angle of rotation for a square.

Solution:

Order of rotational symmetry = 44, Angle of rotation = 90∘90^\circ.

Explanation:

A square looks exactly the same after rotations of 90∘90^\circ, 180∘180^\circ, 270∘270^\circ, and 360∘360^\circ. Since it matches its original shape 44 times in a full circle, the order is 44. Using the formula: 360∘4=90∘\frac{360^\circ}{4} = 90^\circ.

Problem 2:

A figure has an angle of rotation of 120∘120^\circ. Calculate its order of rotational symmetry.

Solution:

Order of rotational symmetry = 33.

Explanation:

Using the formula: Order=360∘120∘=3\text{Order} = \frac{360^\circ}{120^\circ} = 3. This is typically seen in an equilateral triangle.

Problem 3:

Determine the order of rotational symmetry for a rectangle.

Solution:

Order of rotational symmetry = 22.

Explanation:

A rectangle looks identical to the original only after a rotation of 180∘180^\circ and 360∘360^\circ. Therefore, it fits onto itself twice in a full turn.

Problem 4:

Identify the order of rotational symmetry for the letter 'H'.

Solution:

Order of rotational symmetry = 22.

Explanation:

When the letter 'H' is rotated about its center, it looks the same at 180∘180^\circ and 360∘360^\circ. Thus, its order of rotational symmetry is 22.