NCERT Class 7 Maths 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.
Answer: Equilateral triangle and Circle are the 2 figures that have both 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.
Answer:
Line symmetry

Rotational symmetry

(ii) A triangle with only line symmetry and no rotational symmetry of order more than 1.
Answer:

(iii) A quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.
Answer: A quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry cannot be drawn as a quadrilateral with a line symmetry may have rotational symmetry of order one but not more than one.

(iv) A quadrilateral with line symmetry but not a rotational symmetry of order more than 1.
Answer:

Question 3: If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?
Answer: Yes, if a figure has two or more lines of symmetry, then it will have rotational symmetry of order more than 1.

Question 4: Fill in the blanks:

Shape	Centre of Rotation	Order of Rotation	Angle of Rotation
Square
Rectangle
Rhombus
Equilateral Triangle
Regular Hexagon
Circle
Semi-circle

Answer:

Shape	Centre of Rotation	Order of Rotation	Angle of Rotation
Square	Intersecting point of diagonals	4	90o
Rectangle	Intersecting point of diagonals	2	180o
Rhombus	Intersecting point of diagonals	2	180o
Equilateral Triangle	Intersecting point of medians	3	120o
Regular Hexagon	Intersecting point of diagonals	6	60o
Circle	Centre	Infinite	Every angle
Semi-circle	Mid-point of diameter	1	360o

Question 5: Name the quadrilaterals which have both line and rotational symmetry of order more than 1.
Answer: The quadrilateral which have both line and rotational symmetry of order more than 1 is a square.
Line symmetry:

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?
Answer: The other angles are 120°, 180°, 240°, 300°, and 360°.

Question 7: Can we have a rotational symmetry of order more than 1 whose angle of rotation is
(i) 45°?
Answer: Yes, it is possible to have a rotational symmetry of order more than 1 whose angle of rotation is 45°.

(ii) 17°?
Answer: No, it is not possible to have a rotational symmetry of order more than 1 whose angle of rotation is 17°.