Class 7 Exam > Class 7 Notes > Mathematics (Maths) Class 7 > RD Sharma Solutions: Symmetry (Exercise 18.3)
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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.
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