NCERT Solutions for Class 6 Maths Chapter 13 Symmetry
NCERT class 6 maths chapter 13 symmetry exercise: 13.1
Question: 1 List any four symmetrical objects from your home or school.
Answer: Examples of symmetrical objects that we use in our home or school are as follows:
Book, DVD, spectacles, compass, etc.
Question: 2 For the given figure, which one is the mirror line, 
Answer: From the figure we can say that line
Because, when the figure is completely folded about the line
Question: 3 Identify the shapes given below. Check whether they are symmetric or not. Draw the line of symmetry as well.
Answer: (a) Yes, it is symmetrical.
And the line of symmetry is shown in the figure.
(b) Yes, it is symmetrical.
And the line of symmetry is shown in the figure.
(c) No , it is not symmetrical hence there is no line of symmetry in it.
(d) Yes, it is symmetrical.
And the line of symmetry is shown in the figure.
(e) Yes, it is symmetrical.
And the line of symmetry is shown in the figure.
(f) Yes, it is symmetrical.
And the line of symmetry is shown in the figure.
Question: 4 Copy the following on a squared paper. A square paper is what you would have used in your arithmetic notebook in earlier classes. Then complete them such that the dotted line is the line of symmetry.
Answer: After the completion of the above-given figures, we obtain the following figures.
(a)
(b)
(c)
(d)
(e)
(f)
Question: 5 In the figure, l is the line of symmetry. Complete the diagram to make it symmetric.
Answer: The given figure can be completed as follows:
Question: 6 In the figure, l is the line of symmetry. Draw the image of the triangle and complete the diagram so that it becomes symmetric.
Answer: The above diagram can be completed as follows:
NCERT for class 6 maths chapter 13 symmetry exercise 13.2
Question: 1 Find the number of lines of symmety for each of the following shapes :
Answer: The number of lines of symmetry for each of the following shapes is given:
(a)
The given figure has 4 lines of symmetry
(b) .
The given figure has 4 lines of symmetry.
(c)
The given figure has 4 lines of symmetry
(d)
The given figure has only 1 line of symmetry.
(e)
The given figure has 6 lines of symmetry.
(f)
The given figure has 6 lines of symmetry.
(g)
The given figure is asymmetrical and thus, there is no line of symmetry .
(h)
The given figure is asymmetrical and thus, there is no line of symmetry .
(i)
The given figure has 5 lines of symmetry.
Question: 2 Copy the triangle in each of the following figures on squared paper. In each case, draw the line(s) of symmetry, if any and identify the type of triangle. (Some of you may like to trace the figures and try paper-folding first!)
Answer: (a) The line of symmetry of the given figure:
There is only one line of symmetry therefore, it is an isosceles triangle.
(b) The line of symmetry of the given figure:
There is only one line of symmetry therefore, it is an isosceles triangle.
(c) The line of symmetry of the given figure:
There is only one line of symmetry and an angle is right-angled therefore, it is a right-angled isosceles triangle.
(d) The line of symmetry of the given figure:
There is no line of symmetry therefore, it is a scalene triangle.
Question:3 Complete the following table.
|
Shape |
Rough figure |
Number of lines of symmetry |
|
Equilateral triangle |
|
3 |
|
Square |
||
|
Rectangle |
||
|
Isosceles triangle |
||
|
Rhombus |
||
|
Circle |
Answer: The completed table is shown below:
|
Shape |
Rough Figure |
No. of lines of symmetry |
|
Equilateral triangle |
|
3 |
|
Square |
|
4 |
|
Rectangle |
|
2 |
|
Isosceles Triangle |
|
1 |
|
Rhombus |
|
2 |
|
Circle |
|
Infinite or countless |
Question: 4 Can you draw a triangle which has
(a) exactly one line of symmetry?
(b) exactly two lines of symmetry?
(c) exactly three lines of symmetry?
(d) no lines of symmetry?
Sketch a rough figure in each case.
Answer: (a) Yes, with one line of symmetry we have the triangle:
This is an isosceles triangle.
(b) No, as there exists no triangle with only two symmetry lines.
Hence, no such triangle is possible.
(c) Yes, a triangle with three lines of symmetry is possible:
And it is an equilateral triangle, shown below in the figure.
(d) Yes, the triangle with no line of symmetry is possible and it is a scalene triangle:
Shown below,
Question: 5 On a squared paper, sketch the following:
(a) A triangle with a horizontal line of symmetry but no vertical line of symmetry.
(b) A quadrilateral with both horizontal and vertical lines of symmetry.
(c) A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry.
(d) A hexagon with exactly two lines of symmetry.
(e) A hexagon with six lines of symmetry.
( Hint: It will be helpful if you first draw the lines of symmetry and then complete the figures.)
Answer: (a) Triangle with only one line of symmetry is the horizontal line of symmetry and no vertical line of symmetry.
Hence, for the given case,
The triangle can be drawn as:
(b) The quadrilateral which has both the horizontal line and the vertical line of symmetry.
Hence, for the given case:
The quadrilateral can be drawn as:
(c) The quadrilateral which has only one line of symmetry that is:
The horizontal line of symmetry and No, vertical line of symmetry.
Hence, for the given case we have:
The quadrilateral can be drawn as:
(d) The hexagon which has exactly two lines of symmetry that is:
The horizontal line of symmetry and the vertical line of symmetry.
Hence, for the given case, we have the hexagon can be drawn as:
(e) The hexagon has all six lines of symmetry.
First, draw the six lines of symmetry and then complete the hexagon.
Hence, for the given case,
The hexagon can be drawn as:
Question: 6 Trace each figure and draw the lines of symmetry if any:
Answer: (a) The given figure is asymmetrical. Hence, there is no possibility of the line of symmetry.
(b) By observation, the given figure has two squares having a common vertex.
Hence, there are two lines of symmetry possible.
(c) By observation, the given figure has two squares with a common centre.
Hence, the given figure will have four lines of symmetry.
(d) By observation, the given is octagonal.
Hence, it will have two lines of symmetry.
(e) By observation, the given figure is not any specific.
Hence, It will have only one line of symmetry.
(f) Here, we can observe that the given figure is a four-cornered figure.
Hence, it will have four lines of symmetry.
Question: 7 Consider the letters of English alphabets, A to Z. List among them the letters which have
(a) vertical lines of symmetry (like A)
(b) horizontal lines of symmetry (like B)
(c) no lines of symmetry (like Q)
Answer: (a) The letters having the vertical line of symmetry are as follows:
A, H, I, M, O, T, U, V, W, X, Y
(b) The letters having the horizontal line of symmetry are as follows:
B, C, D, E, H, I, K, O, X
(c) The letters that have no line of symmetry are as follows:
F, G, J, L, N, P, Q, R, S, Z
Question: 8 Given here are figures of a few folded sheets and designs drawn about the fold. In each case, draw a rough diagram of the complete figure that would be seen when the design is cut off.
Answer: By observation, we can complete the given figure as follows:
NCER class 6 maths chapter 13 symmetry topic 13.5 reflection and symmetry
Question: If you are 100 cm in front of a mirror, where does your image appear to be? If you move towards the mirror, how does your image move?
Answer: The image appears to be 200 cm away from us, i.e., 100 cm on the other of the mirror.
And if we move towards the mirror, the image moves closer to us and to the mirror, but the size remains the same.
NCERT Class 6 maths chapter 13 symmetry exercise 13.3
Question: 1 Find the number of lines of symmetry in each of the following shapes. How will you check your answers?
Answer: (a) From the given figure, we can observe that,
There are 4 lines of symmetry in the given figure and the lines of symmetry can be shown as:
(b) From the given figure, we can observe that,
There is only 1 line of symmetry in the given figure and it can be drawn as follows:
(c) From the given figure, we can observe that,
There are two lines of symmetry in the given figure and it can be drawn as follows:
(d) From the given figure, we can observe that,
There are two lines of symmetry and it can be drawn as follows:
(e) From the given figure, we can observe that,
There is only one line of symmetry possible and it can be drawn as follows:
(f) From the given figure, we can observe that,
There are 2 lines of symmetry possible in the given figure and it can be drawn as follows:
Question: 2 Copy the following drawing on squared paper. Complete each one of them such that the resulting figure has two dotted lines as two lines of symmetry.
How did you go about completing the picture?
Answer: (a) The given figure can be completed with the help of two symmetric lines i.e., horizontal and vertical lines of symmetry.
Therefore, the completed figure is shown as follows:
(b) We can complete the figure with the help of horizontal and vertical lines of symmetry.
Therefore, the above-given figure can be completed as follows:
(c) The given figure can be completed with the help of horizontal and vertical lines of symmetry.
Therefore, the completed figure is shown below:
(d) The given figure can be completed with the help of horizontal and vertical lines of symmetry.
Therefore, the completed figure is shown below:
(e) The same parts can be drawn to complete the given figure with the help of horizontal and vertical lines of symmetry.
Therefore, the completed figure is shown below:
(f) The same parts can be drawn to complete the given figure with the help of horizontal and vertical lines of symmetry.
Therefore, the completed figure is shown below:
Question:3 In each figure alongside, a letter of the alphabet is shown along with a vertical line. Take the mirror image of the letter in the given line. Find which letters look the same after reflection (i.e. which letters look the same in the image) and which do not. Can you guess why?
Try for
Answer: Mirror images for the given figures are shown as follows:
So, from the above-drawn figures, we can say that the figures having the vertical line of symmetry will have the same mirror images and the letters are:
O, M, H, T, V, X
Thus, the mirror images of these letters will look the same.
