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°