NCERT Solutions Class 7 Math Chapter 12 Symmetry Exercise 12.3

May 14, 2022

NCERT Solutions Class 7 Math Chapter 12 Symmetry Exercise 12.3

Textbook	NCERT
Class	7^th
Subject	Math
Chapter	12^th
Chapter Name	Symmetry
Category	Class 7th Math Solutions
Medium	English
Source	Last Doubt

NCERT Solutions Class 7 Math Chapter 12 Symmetry Exercise 12.3

Chapter – 12

Symmetry

Exercise 12.3

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.
Ch 14 14.3

(ii) Not possible.

Ch 14 14.3
(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:
Ch 14 14.3

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