Exercise 14.3
Question 1:
Name any two figures that have both line symmetry and rotational symmetry.
Answer 1:
Circle and Square.
Question 2:
Draw, wherever possible, a rough sketch of:
(i) a triangle with both line and rotational symmetries of order more than 1.
(ii) a triangle with only line symmetry and no rotational symmetry of order more than 1.
(iii) a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.
(iv) a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.
Answer 2:
(i) An equilateral triangle has both line and rotational symmetries of order more than 1.
Line symmetry:
Rotational symmetry:
(ii) An isosceles triangle has only one line of symmetry and no rotational symmetry of order more than 1.
Line symmetry:
Rotational symmetry:
(iii) It is not possible because order of rotational symmetry is more than 1 of a figure, most acertain the line of symmetry.
(iv) A trapezium which has equal nonparallel sides, a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.
Line symmetry:
Rotational symmetry:
Question 3:
In a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?
Answer 3:
Yes, because every line through the centre forms a line of symmetry and it has rotational symmetry around the centre for every angle.
Question 4:
Fill in the blanks:
Shape  Centre of Rotation  Order of Rotation  Angle of Rotation 
Square 

 
Rectangle 

 
Rhombus 

 
Equilateral triangle 

 
Regular hexagon 

 
Circle 

 
Semicircle 
Answer 4:
Shape  Centre of Rotation  Order of Rotation  Angle of Rotation 
Square  Intersecting point of diagonals.  4  90° 
Rectangle  Intersecting point of diagonals.  2  180° 
Rhombus  Intersecting point of diagonals.  2  180° 
Equilateral triangle  Intersecting point of medians.  3  120° 
Regular hexagon  Intersecting point of diagonals.  6  60° 
Circle  Centre  infinite  At every point 
Semicircle  Midpoint of diameter  1  360° 
Question 5:
Name the quadrilateral which has both line and rotational symmetry of order more than 1.
Answer 5:
Square has both line and rotational symmetry of order more than 1.
Line symmetry:
Rotational symmetry:
Question 6:
After rotating by 60^{o} about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?
Answer 6:
Other angles will be 120°, 180°,240°,300°,360°.
For 60° rotation:
It will rotate six times.
For 120° rotation:
It will rotate three times.
For 180° rotation:
It will rotate two times.
For 360° rotation:
It will rotate one time.
Question 7:
Can we have a rotational symmetry of order more than 1 whose angle of rotation is:
(i) 45^{o}
(ii) 17^{o} ?
Answer 7:
(i) If tiie angle of rotation is 45°, then symmetry of order is possible and would be 8 rotations.
(ii) If the angle of rotational is 17°, then symmetry o f order is not possible because 360° is not complete divided by 17°.