NCERT Exemplar Solutions for Class 6 Maths Chapter 9 Symmetry and Practical Geometry are available in PDF here. Complex problems included in the solutions will assist students in developing problem-solving and higher-order thinking skills. It aims to provide students with a variety of quality problems in different formats, such as multiple-choice questions, short and long answer questions and skill-developing questions. Students who wish to score good marks in Maths can practise NCERT Exemplar Solutions for Class 6 Maths regularly.
In Chapter 9 – Symmetry and Practical Geometry, a figure is said to have line symmetry if, by folding the figure along a line, the left and right parts of it coincide exactly. The line is called the line (or axis) of the symmetry of the figure. In this chapter, students will learn about line symmetry and mirror reflection. Many constructions can be made using different instruments of a geometry box.
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Exercise Page: 136
In questions 1 to 17, out of the given four options, only one is correct. Write the correct answer.
1. In the following figures, the figure that is not symmetric with respect to any line is:
(A) (i) (B) (ii) (C) (iii) (D) (iv)
Solution:-
(B) (ii)
A figure is said to have line symmetry if, by folding the figure along a line, the left and right parts of it coincide exactly. The line is called the line (or axis) of the symmetry of the figure.
2. The number of lines of symmetry in a scalene triangle is
(A) 0 (B) 1 (C) 2 (D) 3
Solution:-
(A) 0
A scalene triangle is a triangle that has three unequal sides.
Therefore, there are no lines of symmetry in a scalene triangle.
3. The number of lines of symmetry in a circle is
(A) 0 (B) 2 (C) 4 (D) more than 4
Solution:-
(D) more than 4
4. Which of the following letters does not have a vertical line of symmetry?
(A) M (B) H (C) E (D) V
Solution:-
(C) E
5. Which of the following letters have both horizontal and vertical lines of symmetry?
(A) X (B) E (C) M (D) K
Solution:-
(A) X
6. Which of the following letters does not have any line of symmetry?
(A) M (B) S (C) K (D) H
Solution:-
(B) S
7. Which of the following letters has only one line of symmetry?
(A) H (B) X (C) Z (D) T
Solution:-
(D) T
8. The instrument to measure an angle is a
(A) Ruler (B) Protractor (C) Divider (D) Compasses
Solution:-
(B) Protractor
An instrument for measuring angles, typically in the form of a flat semicircle marked with degrees along the curved edge.
9. The instrument to draw a circle is
(A) Ruler (B) Protractor (C) Divider (D) Compasses
Solution:-
(D) Compasses
The instrument to draw a circle is a compass.
10. Number of set squares in the geometry box is
(A) 0 (B) 1 (C) 2 (D) 3
Solution:-
(C) 2
11. The number of lines of symmetry in a ruler is
(A) 0 (B) 1 (C) 2 (D) 4
Solution:-
(C) 2
We know that the ruler has the shape of a rectangle,
So, the number of lines of symmetry in a ruler is 2.
12. The number of lines of symmetry in a divider is
(A) 0 (B) 1 (C) 2 (D) 3
Solution:-
(B) 1
The number of lines of symmetry in a divider is 1.
13. The number of lines of symmetry in compasses is
(A) 0 (B) 1 (C) 2 (D) 3
Solution:-
(A) 0
Therefore, there are no lines of symmetry in a compass.
14. The number of lines of symmetry in a protractor is
(A) 0 (B) 1 (C) 2 (D) more than 2
Solution:-
(B) 1
Therefore, there is only one line of symmetry in a protractor.
15. The number of lines of symmetry in a 45o – 45o – 90o set square is
(A) 0 (B) 1 (C) 2 (D) 3
Solution:-
(B) 1
From the question, it is given that the measurement of an isosceles triangle.
So, the number of lines of symmetry in the given set-square is 1.
16. The number of lines of symmetry in a 30o – 60o – 90o set square is
(A) 0 (B) 1 (C) 2 (D) 3
Solution:-
(A) 0
From the question, it is given that measurement of a scalene triangle.
So, the number of lines of symmetry in the given set-square is 0.
17. The instrument in the geometry box having the shape of a triangle is called a
(A) Protractor (B) Compasses
(C) Divider (D) Set-square
Solution:-
(D) Set-square
In questions 18 to 42, fill in the blanks to make the statements true.
18. The distance of the image of a point (or an object) from the line of symmetry (mirror) is ________ as that of the point (object) from the line (mirror).
Solution:-
The distance of the image of a point (or an object) from the line of symmetry (mirror) is the same as that of the point (object) from the line (mirror).
19. The number of lines of symmetry in a picture of the Taj Mahal is _______.
Solution:-
The number of lines of symmetry in a picture of the Taj Mahal is one.
20. The number of lines of symmetry in a rectangle and a rhombus are ______ (equal/unequal).
Solution:-
The number of lines of symmetry in a rectangle and a rhombus are equal.
21. The number of lines of symmetry in a rectangle and a square are______ (equal/unequal).
Solution:-
The number of lines of symmetry in a rectangle and a square are unequal.
22. If a line segment of length 5cm is reflected in a line of symmetry (mirror), then its reflection (image) is a ______ of length _______.
Solution:-
If a line segment of length 5cm is reflected in a line of symmetry (mirror), then its reflection (image) is a line segment of length 5cm.
23. If an angle of measure 80o is reflected in a line of symmetry, then the reflection is an ______ of measure _______.
Solution:-
If an angle of measure 80o is reflected in a line of symmetry, then the reflection is an angle of measure 80o.
24. The image of a point lying on a line l with respect to the line of symmetry l lies on _______.
Solution:-
The image of a point lying on a line l with respect to the line of symmetry l lies on line l.
25. In Fig. 9.10, if B is the image of point A with respect to the line l and P is any point lying on l, then the lengths of line segments PA and PB are _______.
Solution:-
In Fig. 9.10, if B is the image of point A with respect to line l and P is any point lying on l, then the lengths of line segments PA and PB are equal.
26. The number of lines of symmetry in Fig. 9.11 is__________.
Solution:-
The number of lines of symmetry in Fig. 9.11 is 5.
27. The common properties in the two set-squares of a geometry box are that they have a __________ angle and they are of the shape of a __________.
Solution:-
The common properties in the two set-squares of a geometry box are that they have a right angle and they are of the shape of a triangle.
28. The digits having only two lines of symmetry are_________ and __________.
Solution:-
The digits having only two lines of symmetry are 0 and 8.
29. The digit having only one line of symmetry is __________.
Solution:-
The digit having only one line of symmetry is 3.
30. The number of digits having no line of symmetry is_________.
Solution:-
The number of digits having no line of symmetry is 7.
The digits having no line of symmetry are 1, 2, 4, 5, 6, 7 and 9
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