NCERT Exemplar Solutions: Practical Geometry Symmetry & Visualising Solid Shapes | Mathematics for Grade 7 PDF Download

 Page 1


 
Exercise 
 
In each of the Questions 1 to 26, there are four options, out of 
which one is correct. Choose the correct one. 
 
1. A triangle can be constructed by taking its sides as:  
(a) 1.8 cm, 2.6 cm, 4.4 cm       (b) 2 cm, 3 cm, 4 cm  
(c) 2.4 cm, 2.4 cm, 6.4 cm       (d) 3.2 cm, 2.3 cm, 5.5 cm 
 
Solution: 
The condition for constructing a triangle is that Sum of two sides should be greater than the 
third side. And option (b) clearly satisfies this condition as  
(2 + 3) cm > 4 cm.  
 
So, option (b) is correct. 
 
2. A triangle can be constructed by taking two of its angles as:  
(a) 110°, 40°       (b) 70°, 115°       (c) 135°, 45°       (d) 90°, 90° 
 
Solution: 
The condition for constructing a triangle in terms of angle is that sum of all of its angle is 
equal to 180° so sum of two of its angle should be less than 180° respectively. 
In option (a) clearly 110° + 40° = 150° but in rest of the options it is either 180° or greater. 
 
So, option (a) is correct. 
 
3. The number of lines of symmetry in the figure given below is:  
(a) 4       (b) 8       (c) 6       (d) Infinitely many 
 
 
Solution: 
As observed in the given figure, number of lines of symmetry are 6. 
 
So, option (c) is correct. 
 
Chapter - 12 
Practical Geometry Symmetry and Visualizing Solid Shapes 
Page 2


 
Exercise 
 
In each of the Questions 1 to 26, there are four options, out of 
which one is correct. Choose the correct one. 
 
1. A triangle can be constructed by taking its sides as:  
(a) 1.8 cm, 2.6 cm, 4.4 cm       (b) 2 cm, 3 cm, 4 cm  
(c) 2.4 cm, 2.4 cm, 6.4 cm       (d) 3.2 cm, 2.3 cm, 5.5 cm 
 
Solution: 
The condition for constructing a triangle is that Sum of two sides should be greater than the 
third side. And option (b) clearly satisfies this condition as  
(2 + 3) cm > 4 cm.  
 
So, option (b) is correct. 
 
2. A triangle can be constructed by taking two of its angles as:  
(a) 110°, 40°       (b) 70°, 115°       (c) 135°, 45°       (d) 90°, 90° 
 
Solution: 
The condition for constructing a triangle in terms of angle is that sum of all of its angle is 
equal to 180° so sum of two of its angle should be less than 180° respectively. 
In option (a) clearly 110° + 40° = 150° but in rest of the options it is either 180° or greater. 
 
So, option (a) is correct. 
 
3. The number of lines of symmetry in the figure given below is:  
(a) 4       (b) 8       (c) 6       (d) Infinitely many 
 
 
Solution: 
As observed in the given figure, number of lines of symmetry are 6. 
 
So, option (c) is correct. 
 
Chapter - 12 
Practical Geometry Symmetry and Visualizing Solid Shapes 
4. The number of lines of symmetry in Fig. 12.14 is  
(a) 1       (b) 3       (c) 6       (d) infinitely many 
 
 
 
Solution: 
As observed in the given figure, number of lines of symmetry are 3. 
 
So, option (b) is correct. 
 
5. The order of rotational symmetry in the Fig. 12.15 given below is  
(a) 4       (b) 8       (c) 6       (d) infinitely many 
 
 
Solution: 
Rotational symmetry is defined as the no. of times a figure fits into itself in one complete 
turn. As observed in the figure, order of rotational symmetry is 6. 
 
So, option (c) is correct. 
 
6. The order of rotational symmetry in the figure 12.16 given below is  
(a) 4       (b) 2       (c) 1       (d) Infinitely many 
 
 
Solution: 
Rotational symmetry is defined as the no. of times a figure fits into itself in one complete 
turn. As observed in the figure, order of rotational symmetry is 2. 
 
Page 3


 
Exercise 
 
In each of the Questions 1 to 26, there are four options, out of 
which one is correct. Choose the correct one. 
 
1. A triangle can be constructed by taking its sides as:  
(a) 1.8 cm, 2.6 cm, 4.4 cm       (b) 2 cm, 3 cm, 4 cm  
(c) 2.4 cm, 2.4 cm, 6.4 cm       (d) 3.2 cm, 2.3 cm, 5.5 cm 
 
Solution: 
The condition for constructing a triangle is that Sum of two sides should be greater than the 
third side. And option (b) clearly satisfies this condition as  
(2 + 3) cm > 4 cm.  
 
So, option (b) is correct. 
 
2. A triangle can be constructed by taking two of its angles as:  
(a) 110°, 40°       (b) 70°, 115°       (c) 135°, 45°       (d) 90°, 90° 
 
Solution: 
The condition for constructing a triangle in terms of angle is that sum of all of its angle is 
equal to 180° so sum of two of its angle should be less than 180° respectively. 
In option (a) clearly 110° + 40° = 150° but in rest of the options it is either 180° or greater. 
 
So, option (a) is correct. 
 
3. The number of lines of symmetry in the figure given below is:  
(a) 4       (b) 8       (c) 6       (d) Infinitely many 
 
 
Solution: 
As observed in the given figure, number of lines of symmetry are 6. 
 
So, option (c) is correct. 
 
Chapter - 12 
Practical Geometry Symmetry and Visualizing Solid Shapes 
4. The number of lines of symmetry in Fig. 12.14 is  
(a) 1       (b) 3       (c) 6       (d) infinitely many 
 
 
 
Solution: 
As observed in the given figure, number of lines of symmetry are 3. 
 
So, option (b) is correct. 
 
5. The order of rotational symmetry in the Fig. 12.15 given below is  
(a) 4       (b) 8       (c) 6       (d) infinitely many 
 
 
Solution: 
Rotational symmetry is defined as the no. of times a figure fits into itself in one complete 
turn. As observed in the figure, order of rotational symmetry is 6. 
 
So, option (c) is correct. 
 
6. The order of rotational symmetry in the figure 12.16 given below is  
(a) 4       (b) 2       (c) 1       (d) Infinitely many 
 
 
Solution: 
Rotational symmetry is defined as the no. of times a figure fits into itself in one complete 
turn. As observed in the figure, order of rotational symmetry is 2. 
 
So, option (b) is correct. 
 
7. The name of the given solid in Fig 12.17 is:  
(a) Triangular pyramid       (b) rectangular pyramid        
(c) Rectangular prism         (d) triangular prism 
 
 
Solution: 
The given figure as observed is a combination of a rectangle and a pyramid. 
 
So, option (c) is correct. 
 
8. The name of the solid in Fig. 12.18 is:  
(a) triangular pyramid       (b) rectangular prism  
(c) triangular prism            (d) rectangular pyramid 
 
 
Solution: 
The given figure as observed is a combination of a triangle and a prism. 
 
So, option (c) is correct. 
 
9. All faces of a pyramid are always:  
(a) Triangular       (b) Rectangular       (c) Congruent       (d) None of these 
 
Solution: 
Page 4


 
Exercise 
 
In each of the Questions 1 to 26, there are four options, out of 
which one is correct. Choose the correct one. 
 
1. A triangle can be constructed by taking its sides as:  
(a) 1.8 cm, 2.6 cm, 4.4 cm       (b) 2 cm, 3 cm, 4 cm  
(c) 2.4 cm, 2.4 cm, 6.4 cm       (d) 3.2 cm, 2.3 cm, 5.5 cm 
 
Solution: 
The condition for constructing a triangle is that Sum of two sides should be greater than the 
third side. And option (b) clearly satisfies this condition as  
(2 + 3) cm > 4 cm.  
 
So, option (b) is correct. 
 
2. A triangle can be constructed by taking two of its angles as:  
(a) 110°, 40°       (b) 70°, 115°       (c) 135°, 45°       (d) 90°, 90° 
 
Solution: 
The condition for constructing a triangle in terms of angle is that sum of all of its angle is 
equal to 180° so sum of two of its angle should be less than 180° respectively. 
In option (a) clearly 110° + 40° = 150° but in rest of the options it is either 180° or greater. 
 
So, option (a) is correct. 
 
3. The number of lines of symmetry in the figure given below is:  
(a) 4       (b) 8       (c) 6       (d) Infinitely many 
 
 
Solution: 
As observed in the given figure, number of lines of symmetry are 6. 
 
So, option (c) is correct. 
 
Chapter - 12 
Practical Geometry Symmetry and Visualizing Solid Shapes 
4. The number of lines of symmetry in Fig. 12.14 is  
(a) 1       (b) 3       (c) 6       (d) infinitely many 
 
 
 
Solution: 
As observed in the given figure, number of lines of symmetry are 3. 
 
So, option (b) is correct. 
 
5. The order of rotational symmetry in the Fig. 12.15 given below is  
(a) 4       (b) 8       (c) 6       (d) infinitely many 
 
 
Solution: 
Rotational symmetry is defined as the no. of times a figure fits into itself in one complete 
turn. As observed in the figure, order of rotational symmetry is 6. 
 
So, option (c) is correct. 
 
6. The order of rotational symmetry in the figure 12.16 given below is  
(a) 4       (b) 2       (c) 1       (d) Infinitely many 
 
 
Solution: 
Rotational symmetry is defined as the no. of times a figure fits into itself in one complete 
turn. As observed in the figure, order of rotational symmetry is 2. 
 
So, option (b) is correct. 
 
7. The name of the given solid in Fig 12.17 is:  
(a) Triangular pyramid       (b) rectangular pyramid        
(c) Rectangular prism         (d) triangular prism 
 
 
Solution: 
The given figure as observed is a combination of a rectangle and a pyramid. 
 
So, option (c) is correct. 
 
8. The name of the solid in Fig. 12.18 is:  
(a) triangular pyramid       (b) rectangular prism  
(c) triangular prism            (d) rectangular pyramid 
 
 
Solution: 
The given figure as observed is a combination of a triangle and a prism. 
 
So, option (c) is correct. 
 
9. All faces of a pyramid are always:  
(a) Triangular       (b) Rectangular       (c) Congruent       (d) None of these 
 
Solution: 
 
The faces of pyramid can be basically rectangular and triangular. 
 
So, option (d) is correct. 
 
10. A solid that has only one vertex is  
(a) Pyramid       (b) Cube       (c) Cone       (d) Cylinder 
 
Solution: 
A solid that has only one vertex is cone. 
 
 
So, option (c) is correct. 
 
11. Out of the following which is a 3-D figure?  
(a) Square       (b) Sphere       (c) Triangle       (d) Circle 
 
Solution: 
Out of given figures, only sphere is 3-D figure. 
 
So, option (b) is correct. 
 
12. Total number of edges a cylinder has  
(a) 0       (b) 1       (c) 2       (d) 3 
 
Solution: 
Page 5


 
Exercise 
 
In each of the Questions 1 to 26, there are four options, out of 
which one is correct. Choose the correct one. 
 
1. A triangle can be constructed by taking its sides as:  
(a) 1.8 cm, 2.6 cm, 4.4 cm       (b) 2 cm, 3 cm, 4 cm  
(c) 2.4 cm, 2.4 cm, 6.4 cm       (d) 3.2 cm, 2.3 cm, 5.5 cm 
 
Solution: 
The condition for constructing a triangle is that Sum of two sides should be greater than the 
third side. And option (b) clearly satisfies this condition as  
(2 + 3) cm > 4 cm.  
 
So, option (b) is correct. 
 
2. A triangle can be constructed by taking two of its angles as:  
(a) 110°, 40°       (b) 70°, 115°       (c) 135°, 45°       (d) 90°, 90° 
 
Solution: 
The condition for constructing a triangle in terms of angle is that sum of all of its angle is 
equal to 180° so sum of two of its angle should be less than 180° respectively. 
In option (a) clearly 110° + 40° = 150° but in rest of the options it is either 180° or greater. 
 
So, option (a) is correct. 
 
3. The number of lines of symmetry in the figure given below is:  
(a) 4       (b) 8       (c) 6       (d) Infinitely many 
 
 
Solution: 
As observed in the given figure, number of lines of symmetry are 6. 
 
So, option (c) is correct. 
 
Chapter - 12 
Practical Geometry Symmetry and Visualizing Solid Shapes 
4. The number of lines of symmetry in Fig. 12.14 is  
(a) 1       (b) 3       (c) 6       (d) infinitely many 
 
 
 
Solution: 
As observed in the given figure, number of lines of symmetry are 3. 
 
So, option (b) is correct. 
 
5. The order of rotational symmetry in the Fig. 12.15 given below is  
(a) 4       (b) 8       (c) 6       (d) infinitely many 
 
 
Solution: 
Rotational symmetry is defined as the no. of times a figure fits into itself in one complete 
turn. As observed in the figure, order of rotational symmetry is 6. 
 
So, option (c) is correct. 
 
6. The order of rotational symmetry in the figure 12.16 given below is  
(a) 4       (b) 2       (c) 1       (d) Infinitely many 
 
 
Solution: 
Rotational symmetry is defined as the no. of times a figure fits into itself in one complete 
turn. As observed in the figure, order of rotational symmetry is 2. 
 
So, option (b) is correct. 
 
7. The name of the given solid in Fig 12.17 is:  
(a) Triangular pyramid       (b) rectangular pyramid        
(c) Rectangular prism         (d) triangular prism 
 
 
Solution: 
The given figure as observed is a combination of a rectangle and a pyramid. 
 
So, option (c) is correct. 
 
8. The name of the solid in Fig. 12.18 is:  
(a) triangular pyramid       (b) rectangular prism  
(c) triangular prism            (d) rectangular pyramid 
 
 
Solution: 
The given figure as observed is a combination of a triangle and a prism. 
 
So, option (c) is correct. 
 
9. All faces of a pyramid are always:  
(a) Triangular       (b) Rectangular       (c) Congruent       (d) None of these 
 
Solution: 
 
The faces of pyramid can be basically rectangular and triangular. 
 
So, option (d) is correct. 
 
10. A solid that has only one vertex is  
(a) Pyramid       (b) Cube       (c) Cone       (d) Cylinder 
 
Solution: 
A solid that has only one vertex is cone. 
 
 
So, option (c) is correct. 
 
11. Out of the following which is a 3-D figure?  
(a) Square       (b) Sphere       (c) Triangle       (d) Circle 
 
Solution: 
Out of given figures, only sphere is 3-D figure. 
 
So, option (b) is correct. 
 
12. Total number of edges a cylinder has  
(a) 0       (b) 1       (c) 2       (d) 3 
 
Solution: 
 
Cylinder possesses only two edges. 
 
So, option (c) is correct. 
 
13. A solid that has two opposite identical faces and other faces as 
parallelograms is a  
(a) prism       (b) pyramid       (c) cone       (d) sphere 
 
Solution: 
A solid that has two opposite identical faces and other faces as parallelograms is a prism. 
 
 
So, option (a) is correct. 
 
14. The solid with one circular face, one curved surface and one vertex is 
known as:  
(a) cone       (b) sphere       (c) cylinder       (d) prism 
 
Solution: 
The solid with one circular face, one curved surface and one vertex is known as cone.