The DAV Class 8 Maths Solution and **DAV Class 8 Maths Chapter 16 Brain Teasers **Solutions of Rotational Symmetry offer comprehensive answers to textbook questions.

## DAV Class 8 Maths Ch 16 Brain Teasers Solutions

Question 1A.

Tick (✓) the correct option.

(i) How does the shape look like after it rotates 180°?

(a)

(b)

(c)

(d)

Solution:

(b)

Thus, option (b) is the correct answer.

(ii) Letter ‘T’ has rotational symmetry of order

(a) 1

(b) 2

(c) 3

(d) 4

Solution:

(b) 2

The given letter has rotational symmetry of order 2.

Thus, option (b) is the correct answer.

(iii) The angle of rotation of a figure is 36° so, its order of rotational symmetry is

(a) 1

(b) 9

(c) 10

(d) 1

Solution:

(c) 10

Order of Rotational symmetry = \(\frac{360^{\circ}}{\text { Angle of rotation }}\)

= \(\frac{360^{\circ}}{36^{\circ}}\) = 10°

Thus, option (c) is the correct answer.

(iv) Regular pentagon has a rotational symmetry of order

(a) 2

(b) 4

(c) 5

(d) 3

Solution:

(c) 5

The regular pentagon has a rotational symmetry of order 5.

Thus, option (c) is the correct answer.

(v) The angle of rotation of the given figure is

(a) 90°

(b) 180°

(c) 270°

(d) 360°

Solution:

(b) 180°

The given figure has the rotational symmetry of order 2.

∴ Angle of rotation of figure = \(\frac{360^{\circ}}{2}\) = 180°

Thus, the option (b) is the correct answer.

Question 1B.

Answer the following questions.

(i) Name two letters of English alphabet which have no rotational symmetry.

Solution:

Letters ‘F’ and ‘G’ of English alphabet have no rotational symmetry. (Answer may vary)

(ii) Find the angle and order of rotational symmetry of the figure given along side.

Solution:

The given figure, repeats itself two times if it is rotated about a fixed point. So, the given figure has rotational symmetry of order 2.

Angle of rotation of the given figure = \(\frac{360^{\circ}}{2}\) = 180°

(iii) Which letters of English alphabet have rotational symmetry of order 2?

Solution:

Letters ‘H’ and ‘S’ of English alphabet have rotational symmetry of order 2. (Answer may vary)

(iv) Does isosceles triangle exhibit rotational symmetry? Give reason.

Solution:

An isosceles triangle does not exhibit rotational symmetry as it does not repeat itself when it is rotated a full turn.

(v) Find the angle of rotation and order of rotation in the figure given along side.

Solution:

The given figure repeats itself three times when it is rotated about a fixed point. So, the given figure has the rotational symmetry of order 3.

Angle of rotation of the given figure = \(\frac{360^{\circ}}{3}\) = 120°

Question 2.

Name one figure each having rotational symmetry of order:

(i) 4

(ii) 2

(iii) 3

(iv) 6

Solution:

(i) Square has the rotational symmetry of order 4.

The Angle of rotation of Square = \(\frac{360^{\circ}}{4}\) = 90°

(ii) The rectangle has the rotational symmetry of order 2.

Angle of rotation of rectangle = \(\frac{360^{\circ}}{2}\) = 180°

(iii) Equilateral triangle has the rotational symmetry of order 3.

Angle of rotation of equilateral triangle = \(\frac{360^{\circ}}{3}\) = 120°

(iv) Regular hexagon has the rotational symmetry of order 6.

Angle of rotation of regular hexagon = \(\frac{360^{\circ}}{6}\) = 60°.

Question 3.

In the word ‘MATHS’ which letter shows rotational symmetry of order 2?

Solution:

Only H shows the rotational symmetry.

Question 4.

List two letters of English alphabets which exhibit both line as well as rotational symmetry.

Solution:

H and O are the alphabet which shows both line and rotational symmetry.

Question 5.

Find the angle of rotation for each of the following.

Solution:

(i) 180°

(ii) 90°

(iii) 72°

(iv) 90°

Question 6.

Write the order of rotational symmetry of a square and equilateral triangle with the help of rough sketches.

Solution:

(i)

From the above figure, the order of symmetry of square is 4.

(ii)

From the above figure, the order of symmetry of equilateral triangle is 3.

### DAV Class 8 Maths Chapter 16 HOTS

Question 1.

Trace the figure below after it has been rotated 60° about the point G.

Solution:

Question 2.

Shade the triangles in the given figure in such a way that a shape is created with rotational symmetry of order 2.

Solution:

### DAV Class 8 Maths Chapter 16 Enrichment Questions

Question 1.

‘Creating designs from transformations’

The word ‘transformation’ refers to a movement or change in geometric shape.

Reflection and rotation are the different kinds of transformations.

Produce patterns by performing the following transformation on the given figure.

(i) Rotation of 90°, 180°, 270° about the vertex A.

Solution:

(ii) A rotation of 90° about the vertex A followed by a reflection about the base of the figure so obtained.

Solution:

Additional Questions:

Question 1.

Which of the following have rotational symmetry?

Solution:

Figures (i), (iii) and (iv) have rotational symmetry about a fixed point.

Question 2.

Find the order of the rotational symmetry of the following shapes.

(a) Square

(b) Equilateral triangle

(c) Rectangle

Solution:

(а) The order of rotational symmetry of a square is 4.

(b) The order of rotational symmetry of equilateral triangle is 3.

(c) The order of rotational symmetry of a rectangle is 4.

Question 3.

Draw the shapes of the figure whose rotational angles are

(a) 90°

Solution:

Square has rotational angle of 90°.

(b) 120°

Solution:

Equilateral triangle has the rotational angle 120°

(c) 180°

Solution:

Straight line has the rotational angle 180°

(d) 360°

Solution:

Circle has the rotational angle 360°.

Question 4.

Find the lines of symmetry of the following figures.

(a) Circle

Solution:

Cricle has unlimited lines of symmetry.

(b) Square

Solution:

Square has 4 lines of symmetry.

Question 5.

Find the number of lines of symmetry of the following figures.

(a)

Solution:

Here, the figure is a square which has 4 lines of symmetry.

(b)

Solution:

Here, the figure is a parallelogram having no lines of symmetry.

(c)

Solution:

Here, the figure is a regular hexagon which has 6 lines of symmetry.

Question 6.

The order of rotation of a square is

(a) 4

(b) 2

(c) 1

(d) 3

Solution:

(a) is correct.

Question 7.

How many lines of symmetry a regular pentagon has?

(a) 6

(b) 5

(c) 7

(d) 8

Solution:

(b) is correct.

Question 3.

What is the order of rotation and angle of rotation for an equilateral triangle?

Solution:

Equilateral triangle has 3 order of rotation and it has angle of rotation 120°.

Multiple Choice Questions:

Question 1.

The lines of symmetry of a circle is

(a) 5

(b) 6

(c) 10

(d) Unlimited

Solution:

(d) Unlimited

Question 2.

The rotational angle of a square is

(a) 180°

(b) 90°

(c) 120°

(d) None of these

Solution:

(b) 90°

Question 3.

The lines of symmetry of a regular pentagon is

(a) 6

(b) 5

(c) 7

(d) 8

Solution:

(b) 5

Question 4.

The lines of symmetry of a regular hexagon is

(a) 4

(b) 6

(c) 8

(d) 12

Solution:

(b) 6

Question 5.

The angle of rotation of an equilateral triangle is

(a) 120°

(b) 100°

(c) 90°

(d) 180°

Solution:

(a) 120°