NCERT Exemplar Solutions: Symmetry & Practical Geometry

### Exercise Page: 136

In questions 1 to 17, out of the given four options, only one is correct. Write the correct answer.
Q.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)
Ans:
b
Solution:
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 symmetry of the figure.

Q.2. The number of lines of symmetry in a scalene triangle is
(A) 0
(B) 1
(C) 2
(D) 3
Ans:
a
Solution:
A scalene triangle is a triangle that has three unequal sides.
Therefore, there is no lines of symmetry in a scalene triangle.

Q.3. The number of lines of symmetry in a circle is
(A) 0
(B) 2
(C) 4
(D) more than 4
Ans:
d

Q.4. Which of the following letters does not have the vertical line of symmetry?
(A) M
(B) H
(C) E
(D) V
Ans:
c
Solution:

Q.5. Which of the following letters have both horizontal and vertical lines of symmetry?
(A) X
(B) E
(C) M
(D) K
Ans:
a
Solution:

Q.6. Which of the following letters does not have any line of symmetry?
(A) M
(B) S
(C) K
(D) H
Ans:
b
Solution:

Q.7. Which of the following letters has only one line of symmetry?
(A) H
(B) X
(C) Z
(D) T
Ans:
d
Solution:

Q.8. The instrument to measure an angle is a
(A) Ruler
(B) Protractor
(C) Divider
(D) Compasses
Ans:
b
Solution:
An instrument for measuring angles, typically in the form of a flat semicircle marked with degrees along the curved edge.

Q.9. The instrument to draw a circle is
(A) Ruler
(B) Protractor
(C) Divider
(D) Compasses
Ans:
d
Solution:
The instrument to draw a circle is compasses.

Q.10. Number of set squares in the geometry box is
(A) 0
(B) 1
(C) 2
(D) 3
Ans:
c

Q.11. The number of lines of symmetry in a ruler is
(A) 0
(B) 1
(C) 2
(D) 4
Ans: c
Solution:
We know that, ruler has shape of rectangle,
So, the number of lines of symmetry in a ruler is 2.

Q.12. The number of lines of symmetry in a divider is
(A) 0
(B) 1
(C) 2
(D) 3
Ans:
b
Solution:
The number of lines of symmetry in a divider is 1.

Q.13. The number of lines of symmetry in compasses is
(A) 0
(B) 1
(C) 2
(D) 3
Ans:
a
Solution:

Therefore, there is no lines of symmetry in a compasses.

Q.14. The number of lines of symmetry in a protractor is
(A) 0
(B) 1
(C) 2
(D) more than 2
Ans:
b
Solution:

Therefore, there is only one line of symmetry in a protractor.

Q.15. The number of lines of symmetry in a 45o – 45o – 90o set-square is
(A) 0
(B) 1
(C) 2
(D) 3
Ans:
b
Solution:

From the question it is given that, measurement of an isosceles triangle.
So, the number of lines of symmetry in given set-square is 1.

Q.16. The number of lines of symmetry in a 30o – 60o – 90o set square is
(A) 0
(B) 1
(C) 2
(D) 3
Ans:
a
Solution:
From the question it is given that, measurement of scalene triangle.
So, the number of lines of symmetry in given set-square is 0.

Q.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
Ans:
d
Solution:
In questions 18 to 42, fill in the blanks to make the statements true.

Q.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).
Ans:
The distance of the image of a point (or an object) from the line of symmetry (mirror) is same as that of the point (object) from the line (mirror).

Q.19. The number of lines of symmetry in a picture of Taj Mahal is ______ .
Ans: The number of lines of symmetry in a picture of Taj Mahal is one.

Q.20. The number of lines of symmetry in a rectangle and a rhombus are ______. (equal/unequal).
Ans:
The number of lines of symmetry in a rectangle and a rhombus are equal.

Q.21. The number of lines of symmetry in a rectangle and a square are ______ (equal/unequal).
Ans:
The number of lines of symmetry in a rectangle and a square are unequal.

Q.22. If a line segment of length 5cm is reflected in a line of symmetry (mirror), then its reflection (image) is a ______ of length ______.
Ans:
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.

Q.23. If an angle of measure 80o is reflected in a line of symmetry, then the reflection is an ______ of measure ______.
Ans:
If an angle of measure 80o is reflected in a line of symmetry, then the reflection is an angle of measure 80o.

Q.24. The image of a point lying on a line l with respect to the line of symmetry l lies on _______.
Ans:
The image of a point lying on a line l with respect to the line of symmetry l lies on line l.

Q.25. In Fig. 9.10, if B is the image of the 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 _______.
Ans: In Fig. 9.10, if B is the image of the 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 equal.

Q.26. The number of lines of symmetry in Fig. 9.11 is ______.
Ans:
The number of lines of symmetry in Fig. 9.11 is 5.

Q.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 ______.
Ans:
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.

Q.28. The digits having only two lines of symmetry are ______ and ______.
Ans:
The digits having only two lines of symmetry are 0 and 8.

Q.29. The digit having only one line of symmetry is ______.
Ans:
The digit having only one line of symmetry is 3.

Q.30. The number of digits having no line of symmetry is ______.
Ans:
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.

The document NCERT Exemplar Solutions: Symmetry & Practical Geometry | Mathematics for Grade 6 is a part of the Grade 6 Course Mathematics for Grade 6.

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## FAQs on NCERT Exemplar Solutions: Symmetry & Practical Geometry - Mathematics for Grade 6

 1. What is symmetry in practical geometry?
Ans. Symmetry in practical geometry refers to a property where an object or shape can be divided into two or more identical parts that mirror each other. This means that if we fold the shape along the line of symmetry, both sides will coincide perfectly.
 2. How do you identify symmetry in a geometric figure?
Ans. To identify symmetry in a geometric figure, we can look for reflectional symmetry. This means that if we draw a line through the figure and the two halves on either side of the line are identical, then the figure has reflectional symmetry. We can also use a mirror to check if the shape reflects itself.
 3. Can all geometric figures have symmetry?
Ans. No, not all geometric figures have symmetry. Some figures may have multiple lines of symmetry, while others may have no lines of symmetry at all. Irregular shapes or figures with random arrangements of sides and angles often do not exhibit symmetry.
 4. What is the importance of symmetry in practical geometry?
Ans. Symmetry in practical geometry plays a significant role in various fields, such as architecture, art, and design. It helps create aesthetically pleasing and balanced structures, patterns, and objects. Symmetry also aids in the analysis and understanding of geometric shapes and their properties.
 5. How can symmetry be used practically in everyday life?
Ans. Symmetry can be used practically in everyday life in many ways. For example, it is utilized in the design of buildings, furniture, and home decor to create visually appealing and harmonious spaces. It is also employed in graphic design, fashion, and even in nature, as many living organisms exhibit symmetrical patterns.

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