Chapter 14 Symmetry Exercise 14.3

Chapter 14 Symmetry Exercise 14.3

Question 1.
Name any two figures that have both line symmetry and rotational symmetry.
Solution:
English alphabet H and O both have line symmetry and rotational symmetry.

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.
Solution:
(i) Equilateral triangle has 3 rotational symmetries.

(ii) Not possible.
(iii) 

(iv) Not possible.

Question 3.
If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?
Solution:

Yes. The above figure has two lines of symmetry and also rotational symmetry of order 2.

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

Solution:

Shape	Centre of rotation	Order of rotation	Angle of rotation
Square	Point of intersection of diagonals	4	90°
Rectangle	Point of intersection of diagonals	4	90°
Rhombus	Point of intersection of diagonals	4	90°
Equilateral triangle	Point of intersection of medians	3	120°
Regular hexagon	Point of intersection of diagonals	6	60°
Circle	Centre	Infinite	Every angle
Semicircle	Centre	4	90°

Question 5.
Name the quadrilaterals which have both line and rotational symmetry of order more than 1.
Solution:
Square, rectangles and rhombus are such quadrilateral which have both line and rotational symmetry.

Question 6.
After rotating by 60° about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?
Solution:
If a figure is rotated through the angles 120°, 180°, 240°, 300° and 360°, it looks exactly the same.

Question 7.

Can we have a rotational symmetry of order more than 1 whose angle of rotation is
(i) 45°?
(ii) 17°?
Solution:
(i) Yes
(ii) No