ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 14 Symmetry Objective Type Questions
Mental Maths
Question 1.
Fill in the blanks:
(i) The hands of a clock rotate only in ………. direction.
(ii) While opening the cap of a bottle, the direction of rotation is ……….
(iii) The number of lines of symmetry of an isosceles right-angled triangle is …………
(iv) A figure has ……….. symmetry if it is its own image under a reflection.
(v) The centre of rotation of an equilateral triangle is the point of intersection of its ………..
(vi) The centre of rotation of a rhombus is the point ……….
(vii) A regular polygon of n-sides has ……….. the number of lines of symmetry.
(viii) The angle of rotational symmetry in an equilateral triangle is ……….
(ix) The angle of rotational symmetry in a regular pentagon is ……..
(x) If after a rotation of 45° about a fixed point the figure looks exactly the same, then the order of rotational symmetry is ……….
Solution:
(i) The hands of a clock rotate only in a clockwise direction.
(ii) While opening the cap of a bottle, the direction of rotation is anticlockwise.
(iii) The number of lines of symmetry of an isosceles right-angled triangle is one.
(iv) A figure has line symmetry if it is its own image under a reflection.
(v) The centre of rotation of an equilateral triangle is
the point of intersection of its medians/angle bisector/altitude.
(vi) The centre of rotation of a rhombus is the point intersection of its diagonals.
(vii) A regular polygon of n-sides has n number of lines of symmetry.
(viii) Angle of rotational symmetry in an equilateral triangle is \(\frac { 360 }{ 3 }\) = 120°.
(ix) Angle of rotational symmetry in a regular pentagon is \(\frac { 360 }{ 5 }\) = 72°.
(x) If after a rotation of 45° about a fixed point the figure looks exactly the same,
then the order of rotational symmetry is \(\frac { 360 }{ 45 }\) = 8.
Question 2.
State whether the following statements are true (T) or false (F):
(i) The letter A has line symmetry but no rotational symmetry.
(ii) A rhombus is also a parallelogram and hence it does not have line symmetry.
(iii) A parallelogram has two lines of symmetry.
(iv) The order of rotational symmetry of a rhombus is four.
(v) A circle has exactly four lines of symmetry.
(vi) In a regular pentagon, the perpendicular bisector of the sides are the only lines of symmetry.
(vii) In a regular hexagon, the perpendicular bisector of the sides are the only lines of symmetry.
(viii) In a rectangle, the angle of rotational symmetry is 90°.
(ix) A semicircle has rotational symmetry of order 2.
(x) An isosceles triangle has neither a line symmetry nor a rotational symmetry.
(xi) If a figure possesses a rotational symmetry, then it must look exactly the same atleast once up to a rotation of 180°.
(xii) The angle of rotation of a figure is obtained by dividing 360° by the order of rotational symmetry.
(xiii) A regular triangle has 3 lines of symmetry and rotational symmetry of order 3.
(xiv) A regular pentagon has 5 lines of symmetry and rotational symmetry of order 5.
Solution:
(i) The letter A has line symmetry but no rotational symmetry. (True)
(ii) A rhombus is also a parallelogram
and hence it does not have line symmetry. (False)
Correct:
As rhombus is a special type of ||gm which has all sides equal.
(iii) A parallelogram has two lines of symmetry. (False)
Correct:
It does not have any line of symmetry.
(iv) The order of rotational symmetry of a rhombus is four. (False)
Correct:
it has two order of rotational symmetry.
(v) A circle has exactly four lines of symmetry. (False)
Correct:
As a circle has infinite lines of symmetry.
(vi) In a regular pentagon,
the perpendicular bisector of the sides are the only lines of symmetry. (True)
(vii) In a regular hexagon,
the perpendicular bisector of the sides are the only lines of symmetry. (False)
Correct:
Its diagonals are also the lines of symmetry.
(viii)In a rectangle, the angle of rotational symmetry is 90°. (False)
Correct:
Its angles are 180°
(ix) A semicircle has rotational symmetry of order 2. (False)
Correct:
It has no order of rotational symmetry.
(x) An isosceles triangle has neither a line symmetry
nor a rotational symmetry. (False)
Correct:
It has one line of symmetry but no rotational symmetry.
(xi) If a figure possesses a rotational symmetry,
then it must look exactly the same at least once up to a rotation of 180°. (True)
(xii) The angle of rotation of a figure is obtained
by dividing 360° by the order of rotational symmetry. (True)
(xiii) A regular triangle has 3 lines of symmetry
and rotational symmetry of order 3. (True)
(xiv) A regular pentagon has 5 lines of symmetry
and rotational symmetry of order 5. (True)
Multiple Choice Questions
Choose the correct answer from the given four options (3 to 14):
Question 3.
A quadrilateral having four lines of symmetry is a
(a) parallelogram
(b) rectangle
(c) rhombus
(d) square
Solution:
A quadrilateral having four lines of symmetry is a square. (d)
Question 4.
The letter Z has
(a) one horizontal line of symmetry
(b) one vertical line of symmetry
(c) two lines of symmetry
(d) no line of symmetry
Solution:
The letter Z has no line of symmetry. (d)
Question 5.
A figure that does not have any rotational symmetry is
(a) circle
(b) parallelogram
(c) kite
(d) regular pentagon
Solution:
A figure that does not have any rotational symmetry is a kite. (c)
Question 6.
The number of lines of symmetry in the given figure is
(a) 1
(b) 3
(c) 6
(d) infinitely many
Solution:
The number of lines of symmetry in the given figure is 3. (b)
Question 7.
Rotating a figure by 60° anticlockwise is equivalent to a clockwise rotation of
(a) 60°
(b) 120°
(c) 240°
(d) 300°
Solution:
Rotating a figure by 60° anti-clockwise is equivalent
to a clockwise rotation of 360° – 60° = 300° (d)
Question 8.
A figure having 1 line of symmetry and whose order of rotational symmetry is also 1 is
(a) rhombus
(b) parallelogram
(c) kite
(d) scalene triangle
Solution:
A figure having 1 line of symmetry and
whose order of rotational symmetry is also 1 is a kite. (c)
Question 9.
The order of rotational symmetry of a line segment is
(a) 1
(b) 2
(c) 3
(d) 4
Solution:
The order of rotational symmetry of a line segment is 2. (b)
Question 10.
The order of the rotational symmetry in the given figure is
(a) 1
(b) 2
(c) 4
(d) infinitely many
Solution:
The order of the rotational symmetry in the given figure is 2. (b)
Question 11.
A possible angle of rotation of a figure having rotational symmetry of order greater than 1 is
(a) 36°
(b) 144°
(c) 150°
(d) 360°
Solution:
A possible angle of rotation of a figure having
rotational symmetry of order greater than 1 is 360°. (d)
Question 12.
The figure which does not have both reflection and rotational symmetry is
Solution:
The figure which does not have
both reflection and rotational symmetry is (c). (c)
Question 13.
In the word ’MATHS’ which of the following pairs of letters have rotational symmetry?
(a) M and T
(b) A and S
(c) T and S
(d) H and S
Solution:
The word ’MATHS’ which of the following
pairs of letters have rotational symmetry H and S. (d)
Question 14.
The letter which has both reflection and rotational symmetry is
(a) H
(b) M
(c) S
(d) Y
Solution:
The letter which has both reflection
and rotational symmetry is H. (a)