Symmetry (Exercise 18.3) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

 Page 1


 
 
 
 
 
 
 
 
        
 
1. Give the order of rotational symmetry for each of the following figures when 
rotated about the marked point (x): 
 
Solution: 
(i) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 4. 
 
(ii) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 3. 
 
Page 2


 
 
 
 
 
 
 
 
        
 
1. Give the order of rotational symmetry for each of the following figures when 
rotated about the marked point (x): 
 
Solution: 
(i) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 4. 
 
(ii) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 3. 
 
 
 
 
 
 
 
 
 
(iii) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 3. 
 
(iv) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 4. 
 
(v) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 2. 
 
(vi) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 4. 
 
(vii) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 5. 
 
(viii) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 6. 
 
(ix) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 3. 
 
2. Name any two figures that have both line symmetry and rotational symmetry. 
 
Solution: 
An equilateral triangle and a square have both lines of symmetry and rotational 
symmetry. 
Page 3


 
 
 
 
 
 
 
 
        
 
1. Give the order of rotational symmetry for each of the following figures when 
rotated about the marked point (x): 
 
Solution: 
(i) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 4. 
 
(ii) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 3. 
 
 
 
 
 
 
 
 
 
(iii) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 3. 
 
(iv) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 4. 
 
(v) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 2. 
 
(vi) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 4. 
 
(vii) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 5. 
 
(viii) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 6. 
 
(ix) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 3. 
 
2. Name any two figures that have both line symmetry and rotational symmetry. 
 
Solution: 
An equilateral triangle and a square have both lines of symmetry and rotational 
symmetry. 
 
 
 
 
 
 
 
 
 
 
3. Give an example of a figure that has a line of symmetry but does not have 
rotational symmetry. 
 
Solution: 
A semicircle and an isosceles triangle have a line of symmetry but do not have rotational 
symmetry. 
 
 
4. Give an example of a geometrical figure which has neither a line of symmetry nor a 
rotational symmetry. 
 
Solution: 
A scalene triangle has neither a line of symmetry nor a rotational symmetry. 
Page 4


 
 
 
 
 
 
 
 
        
 
1. Give the order of rotational symmetry for each of the following figures when 
rotated about the marked point (x): 
 
Solution: 
(i) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 4. 
 
(ii) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 3. 
 
 
 
 
 
 
 
 
 
(iii) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 3. 
 
(iv) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 4. 
 
(v) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 2. 
 
(vi) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 4. 
 
(vii) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 5. 
 
(viii) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 6. 
 
(ix) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 3. 
 
2. Name any two figures that have both line symmetry and rotational symmetry. 
 
Solution: 
An equilateral triangle and a square have both lines of symmetry and rotational 
symmetry. 
 
 
 
 
 
 
 
 
 
 
3. Give an example of a figure that has a line of symmetry but does not have 
rotational symmetry. 
 
Solution: 
A semicircle and an isosceles triangle have a line of symmetry but do not have rotational 
symmetry. 
 
 
4. Give an example of a geometrical figure which has neither a line of symmetry nor a 
rotational symmetry. 
 
Solution: 
A scalene triangle has neither a line of symmetry nor a rotational symmetry. 
 
 
 
 
 
 
 
 
 
 
5. Give an example of a letter of the English alphabet which has 
(i) No line of symmetry 
(ii) Rotational symmetry of order 2. 
 
Solution: 
(i) The letter of the English alphabet which has no line of symmetry is Z. 
 
(ii) The letter of the English alphabet which has rotational symmetry of order 2 is N. 
 
6. What is the line of symmetry of a semi-circle? Does it have rotational symmetry? 
 
Solution: 
A semicircle (half of a circle) has only one line of symmetry. In the figure, there is one 
line of symmetry. The figure is symmetric along the perpendicular bisector I of the 
diameter XY. A semi-circle does not have any rotational symmetry. 
 
 
7. Draw, whenever possible, a rough sketch of 
(i) a triangle with both line and rotational symmetries. 
(ii) a triangle with only line symmetry and no rotational symmetry. 
(iii) a quadrilateral with a rotational symmetry but not a line of symmetry. 
(iv) a quadrilateral with line symmetry but not a rotational symmetry. 
Page 5


 
 
 
 
 
 
 
 
        
 
1. Give the order of rotational symmetry for each of the following figures when 
rotated about the marked point (x): 
 
Solution: 
(i) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 4. 
 
(ii) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 3. 
 
 
 
 
 
 
 
 
 
(iii) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 3. 
 
(iv) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 4. 
 
(v) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 2. 
 
(vi) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 4. 
 
(vii) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 5. 
 
(viii) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 6. 
 
(ix) A figure is said to have rotational symmetry if its fits onto itself more than once 
during a full turn that is rotation through 360
o
 
Therefore the given figure has its rotational symmetry as 3. 
 
2. Name any two figures that have both line symmetry and rotational symmetry. 
 
Solution: 
An equilateral triangle and a square have both lines of symmetry and rotational 
symmetry. 
 
 
 
 
 
 
 
 
 
 
3. Give an example of a figure that has a line of symmetry but does not have 
rotational symmetry. 
 
Solution: 
A semicircle and an isosceles triangle have a line of symmetry but do not have rotational 
symmetry. 
 
 
4. Give an example of a geometrical figure which has neither a line of symmetry nor a 
rotational symmetry. 
 
Solution: 
A scalene triangle has neither a line of symmetry nor a rotational symmetry. 
 
 
 
 
 
 
 
 
 
 
5. Give an example of a letter of the English alphabet which has 
(i) No line of symmetry 
(ii) Rotational symmetry of order 2. 
 
Solution: 
(i) The letter of the English alphabet which has no line of symmetry is Z. 
 
(ii) The letter of the English alphabet which has rotational symmetry of order 2 is N. 
 
6. What is the line of symmetry of a semi-circle? Does it have rotational symmetry? 
 
Solution: 
A semicircle (half of a circle) has only one line of symmetry. In the figure, there is one 
line of symmetry. The figure is symmetric along the perpendicular bisector I of the 
diameter XY. A semi-circle does not have any rotational symmetry. 
 
 
7. Draw, whenever possible, a rough sketch of 
(i) a triangle with both line and rotational symmetries. 
(ii) a triangle with only line symmetry and no rotational symmetry. 
(iii) a quadrilateral with a rotational symmetry but not a line of symmetry. 
(iv) a quadrilateral with line symmetry but not a rotational symmetry. 
 
 
 
 
 
 
 
 
 
Solution: 
(i) An equilateral triangle has 3 lines of symmetry and a rotational symmetry of order 3. 
 
 
(ii) An isosceles triangle has only 1 line of symmetry and no rotational symmetry. 
 
 
(iii) A parallelogram is a quadrilateral which has no line of symmetry but a rotational 
symmetry of order 2.