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NCERT Solutions for Class 8 Maths - Symmetry- 2

Exercise 14.3 

Question 1: 

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

Answer 1: 

Circle and Square.

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. 

Answer 2: 

(i) An equilateral triangle has both line and rotational symmetries of order more than 1.

Line symmetry:

NCERT Solutions for Class 8 Maths - Symmetry- 2

Rotational symmetry:

NCERT Solutions for Class 8 Maths - Symmetry- 2NCERT Solutions for Class 8 Maths - Symmetry- 2NCERT Solutions for Class 8 Maths - Symmetry- 2

(ii) An isosceles triangle has only one line of symmetry and no rotational symmetry of order more than 1.

Line symmetry:

NCERT Solutions for Class 8 Maths - Symmetry- 2

Rotational symmetry:

NCERT Solutions for Class 8 Maths - Symmetry- 2

(iii) A quadrilateral with no line of symmetry is an irregular quadrilateral
NCERT Solutions for Class 8 Maths - Symmetry- 2

Checking rotational symmetry
If it is rotated 90°
NCERT Solutions for Class 8 Maths - Symmetry- 2

It does not looks same as initial figure
If it is rotated 180°

NCERT Solutions for Class 8 Maths - Symmetry- 2

It does not looks same as initial figure
If it is rotated 360°

NCERT Solutions for Class 8 Maths - Symmetry- 2

It looks same as initial figure
Thus,

NCERT Solutions for Class 8 Maths - Symmetry- 2

Thus, order of rotational symmetry - 1
Hence,
A quadrilateral with a rotational symmetry of order not a line of symmetry Is not possible

(iv) A trapezium which has equal non-parallel sides, a quadrilateral with line symmetry but not a rotational symmetry of order more than 1. 

Line symmetry: 

NCERT Solutions for Class 8 Maths - Symmetry- 2

Rotational symmetry: 

NCERT Solutions for Class 8 Maths - Symmetry- 2

Question 3: 

In a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1? 

Answer 3: 

Yes, because every line through the centre forms a line of symmetry and it has rotational symmetry around the centre for every angle.

 

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 4: 

Shape

Centre of Rotation

Order of Rotation

Angle of Rotation

Square

Intersecting point of diagonals.

4

90°

Rectangle

Intersecting point of diagonals.

2

180°

Rhombus

Intersecting point of diagonals.

2

180°

Equilateral

triangle

Intersecting point of medians.

3

120°

Regular

hexagon

Intersecting point of diagonals.

6

60°

Circle

Centre

infinite

At every point

Semi-circle

Mid-point of diameter

1

360°

 

Question 5: 

Name the quadrilateral which has both line and rotational symmetry of order more than 1. 

Answer 5: 

Square has both line and rotational symmetry of order more than 1.

Line symmetry:  NCERT Solutions for Class 8 Maths - Symmetry- 2

Rotational symmetry:

NCERT Solutions for Class 8 Maths - Symmetry- 2NCERT Solutions for Class 8 Maths - Symmetry- 2

Question 6: 

After rotating by 60o about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure? 

Answer 6: 

Other angles will be 120°, 180°,240°,300°,360°.

For 60° rotation:

It will rotate six times.

NCERT Solutions for Class 8 Maths - Symmetry- 2NCERT Solutions for Class 8 Maths - Symmetry- 2NCERT Solutions for Class 8 Maths - Symmetry- 2

NCERT Solutions for Class 8 Maths - Symmetry- 2NCERT Solutions for Class 8 Maths - Symmetry- 2NCERT Solutions for Class 8 Maths - Symmetry- 2

For 120° rotation:

It will rotate three times.

NCERT Solutions for Class 8 Maths - Symmetry- 2NCERT Solutions for Class 8 Maths - Symmetry- 2NCERT Solutions for Class 8 Maths - Symmetry- 2

For 180° rotation:

It will rotate two times.

NCERT Solutions for Class 8 Maths - Symmetry- 2

For 360° rotation:

It will rotate one time.

NCERT Solutions for Class 8 Maths - Symmetry- 2

Question 7: 

Can we have a rotational symmetry of order more than 1 whose angle of rotation is: 

(i) 45o 
(ii) 17o

Answer 7: 

(i) If tiie angle of rotation is 45°, then symmetry of order is possible and would be 8 rotations.
(ii) If the angle of rotational is 17°, then symmetry o f order is not possible because 360° is not complete divided by 17°.

The document NCERT Solutions for Class 8 Maths - Symmetry- 2 is a part of the Class 7 Course NCERT Textbooks & Solutions for Class 7.
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FAQs on NCERT Solutions for Class 8 Maths - Symmetry- 2

1. What is symmetry?
Ans. Symmetry is a concept in mathematics that refers to a balanced arrangement of parts or objects that can be divided into equal halves or have mirror images. It is a property that many shapes, patterns, and objects possess.
2. How is symmetry useful in daily life?
Ans. Symmetry has several practical applications in daily life. It is used in architecture to create visually appealing buildings, in graphic design to create balanced and harmonious compositions, in fashion and textiles to create patterns and prints, and even in nature to determine the attractiveness of organisms.
3. What are the different types of symmetry?
Ans. There are three main types of symmetry: reflectional symmetry (also known as mirror symmetry), rotational symmetry, and translational symmetry. Reflectional symmetry occurs when an object can be divided into two equal halves that are mirror images of each other. Rotational symmetry occurs when an object can be rotated around a central point and still look the same. Translational symmetry occurs when an object can be shifted or translated without changing its overall appearance.
4. How can symmetry be identified in geometric shapes?
Ans. Symmetry in geometric shapes can be identified by observing if the shape can be divided into equal halves that are mirror images of each other. For example, a square has reflectional symmetry because it can be divided into two equal halves that are mirror images. On the other hand, a rectangle does not have reflectional symmetry because its halves are not mirror images.
5. Can all objects have symmetry?
Ans. No, not all objects have symmetry. While many objects in nature and man-made designs exhibit symmetry, there are also objects that do not possess any symmetrical properties. Irregular shapes, such as rocks or clouds, often lack symmetry. However, symmetry is a common and important characteristic in various fields of study, such as mathematics, art, and biology.
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