NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Ex 14.3

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Ex 14.3

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Ex 14.3

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Ex 14.3 are the part of NCERT Solutions for Class 7 Maths. Here you can find the NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Ex 14.3.



Ex 14.1 Class 7 Maths Question 1.

Name any two figures that have both line symmetry and rotational symmetry.

Solution:
An equilateral triangle and a square both have line symmetry and rotational symmetry.

 

Ex 14.3 Class 7 Maths 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) An equilateral triangle has 3 lines of symmetry and rotational symmetry of order 3.

(ii) An isosceles triangle has one line of symmetry and no rotational symmetry.

(iii) A parallelogram has rotational symmetry of order 2 and no line of symmetry.

(iv) An isosceles trapezium has one line of symmetry and no rotational symmetry.

Ex 14.3 Class 7 Maths 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 is a rectangle. It has two lines of symmetry and also rotational symmetry of order 2.

Ex 14.3 Class 7 Maths 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

 

 

 

 

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

2

180°

Rhombus

Point of intersection of diagonals

2

180°

Equilateral triangle

Point of intersection of medians

3

120°

Regular hexagon

Point of intersection of diagonals

6

60°

Circle

Centre

Infinite

Every angle

Semi-circle

Centre

1

360°

 

Ex 14.3 Class 7 Maths Question 5.

Name the quadrilaterals which have both line and rotational symmetry of order more than 1.

Solution:
A square, a rectangle and a rhombus are such quadrilaterals which have both line and rotational symmetry of order more than 1.

 

Ex 14.3 Class 7 Maths 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:
Since the figure looks exactly the same as its original position, when rotated through 60° about its centre, the angle of rotation is 60°. If the figure is rotated through the angles 120°, 180°, 240°, 300° and 360°, it looks exactly the same.

 

Ex 14.3 Class 7 Maths 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; because 360° is divisible by 45°.
(ii) No; because 360° is not divisible by 17°.

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