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°.

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