Symmetry
Class 6th Mathematics CBSE Solution
- List any four symmetrical objects from your home or school.
- For the given figure, which one is the mirror line, l1 or l2?
- Identify the shapes given below (Text book). Check whether they are symmetric…
- Copy the following on a squared paper. A square paper is what you would have…
- In the figure, l is the line of symmetry. Complete the diagram to make it…
- In the figure, l is the line of symmetry. Draw the image of the triangle and…
- Find the number of lines of symmetry for each of the following shapes:(a) (b)…
- Copy the triangle in each of the following figures on squared paper. In each…
- Complete the following table: Shape Rough figure Number of lines of symmetry…
- Can you draw a triangle which has: (a) Exactly one line of symmetry? (b)…
- On a squared paper, sketch the following: (a) A triangle with a horizontal line…
- Trace each figure and draw the lines of symmetry, if any: (a) (b) (c) (d) (e)…
- Consider the letters of English alphabets, A to Z. List among them the letters…
- Given here are figures of a few folded sheets and designs drawn about the fold.…
Exercise 13.1
Question 1.List any four symmetrical objects from your home or school.
Answer:
Four symmetrical objects that we use in our home or school are as follows:
Paper, Glass, Bucket, CD etc
Question 2.
For the given figure, which one is the mirror line, l1 or l2?
Answer:
In the above given figure line l2 is the mirro line of the figure.
This is because when the figure is folded about the line l2 then the left part will cover the right part completely.
Question 3.
Identify the shapes given below (Text book). Check whether they are symmetric or not. Draw the line of symmetry as well.
Answer:
(a) The given figure is symmetrical and the lines of symmetry in the given figure are as follows:
(b) The given figure is symmetrical and the lines of symmetry in the given figure are as follows:
(c) The given figure is not symmetrical. Hence there are no lines of symmetry in it.
(d) The given figure is symmetrical and the lines of symmetry in the given figure are as follows:
(e) The given figure is symmetrical and the lines of symmetry in the given figure are as follows:
(f) The given figure is symmetrical and the lines of symmetry in the given figure are as follows:
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:
(a) Completion of above given figure is as follow:
(b) Completion of above given figure is as follow:
(c) Completion of above given figure is as follow:
(d) Completion of above given figure is as follow:
(e) Completion of above given figure is as follow:
(f) Completion of above given figure is as follow:
Question 5.
In the figure, l is the line of symmetry. Complete the diagram to make it symmetric.
Answer:
The above given diagram 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:
To make the above diagram symmetric, we can complete it as follows:
Exercise 13.2
Question 1.Find the number of lines of symmetry for each of the following shapes:
(a) 
(b) 
(c) 
(d) 
(e) 
(f) 
(g) 
(h) 
(i) 
Answer:
The following figures have the following 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!)
(a) 
(b) 
(c) 
(d) 
Answer:
(a) At first,
We have to copy the figure,
And, then
We have to draw the line of symmetry if present.
Thus,
Hence,
We can observe that,
There is only one line of symmetry
Therefore,
It is an iscoceles triangle.
(b) At first,
We have to copy the figure,
And, then
We have to draw the line of symmetry if present.
Thus,
Hence,
We can observe that,
There is only one line of symmetry
Therefore,
It is an iscoceles triangle.
(c) At first,
We have to copy the figure,
And, then
We have to draw the line of symmetry if present.
Thus,
Hence,
We can observe that,
There is only one line of symmetry
And,
An angle is right angled
Therefore,
It is a right-angled iscoceles triangle.
(d) At first,
We have to copy the figure,
And, then
We have to draw the line of symmetry if present.
Thus,
Now,
We can observe that there is no line of symmetry possible in the figure.
Hence,
The given triangle is a scalen triangle.
Question 3.
Complete the following table:
Answer:
We can fill the given table as follows:
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?
Answer:
(a) Here,
We have to draw a triangle which has only one line of symmetry.
Hence,
For the given case,
We will draw an iscoceles triangle.
Therefore,
The triangle can be drawn as:
(b) Here,
We have to draw a triangle which has only two lines of symmetry.
But,
We know that,
There exists no triangle with only two symmetry lines.
Hence,
For the given case,
No such triangle is possible.
(c) Here,
We have to draw a triangle which has only three lines of symmetry.
Hence,
For the given case,
We will draw an equilateral triangle.
Therefore,
The triangle can be drawn as:
(d) Here,
We have to draw a triangle which has no line of symmetry.
Hence,
For the given case,
We will draw a scalene triangle.
Therefore,
The triangle can be drawn as:
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.
Answer:
(a) Here,
We have to draw a triangle which has only one line of symmetry that is horizontal line of symmetry
And,
No vertical line of symmetry.
Hence,
For the given case,
The triangle can be drawn as:
(b) Here,
We have to draw a quadrilateral which has both
The horizontal line of symmetry
And,
The vertical line of symmetry
Hence,
For the given case,
The quadrilateral can be drawn as:
(c) Here,
We have to draw a 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,
The quadrilateral can be drawn as:
(d) Here,
We have to draw a 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,
The hexagon can be drawn as:
(e) Here,
We have to draw a hexagon which has in all six lines of symmetry
Now,
In order to draw such hexagon
At first,
We will draw those six lines of symmetry
And, then
We will 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:
(a) 
(b) 
(c) 
(d) 
(e) 
(f) 
Answer:
(a) Here,
At first,
We have to trace the figure
Thus,
Now,
We can obseve that
The given figure is an iscoceles triangle
Hence,
It will have only one line of symmetry.
(b) Here,
At first,
We have to trace the figure
Thus,
Now,
We can obseve that
The given figure has two squares having a common vertex.
Hence,
The figure will have two lines of symmetry.
(c) Here,
At first,
We have to trace the figure
Thus,
Now,
We can obseve that
The given figure has two squares with a common centre
Hence,
The figure will have four lines of symmetry.
(d) Here,
At first,
We have to trace the figure
Thus,
Now,
We can obseve that
The given figure is an octagonal
Hence,
It will have two lines of symmetry.
(e) Here,
At first,
We have to trace the figure
Thus,
Now,
We can obseve that
The given figure is not any specific figure
Hence,
It will have only one line of symmetry.
(f) Here,
At first,
We have to trace the figure
Thus,
Now,
We can obseve 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 that have verticle line of symmetry are as follows:
A, H, I, M, O, T, U, V, W, X, Y
(b) The letters that have 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:
The complete figure will be as follows:
Exercise 13.3
Question 1.Find the number of lines of symmetry in each of the following shapes:
How will you check your answer?
(a) 
(b) 
(c) 
(d) 
(e) 
(f) 
Answer:
(a) From the above given figure, it is clearly observed that,
There are 4 lines of symmetry in the given figure and it can be drawn as follows:
(b) From the above given figure, it is clearly observed that,
There is only 1 line of symmetry in the given figure and it can be drawn as follows:
(c) From the above given figure, it is clearly observed that,
There are 2 lines of symmetry in the given figure and it can be drawn as follows:
(d) From the above given figure, it is clearly observed that,
There are 2 lines of symmetry in the given figure and it can be drawn as follows:
(e) From the above given figure, it is clearly observed that,
There is only 1 line of symmetry in the given figure and it can be drawn as follows:
(f) From the above given figure, it is clearly observed that,
There are 2 lines of symmetry 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 above given figure can be completed by drawing the same parts as shown in the given figure
We can draw this by drawing horizontal and vertical line of symmetry
Therefore,
The above given figure can be completed as follows:
(b) The above given figure can be completed by drawing the same parts as shown in the given figure
We can draw this by drawing horizontal and vertical line of symmetry
Therefore,
The above given figure can be completed as follows:
(c) The above given figure can be completed by drawing the same parts as shown in the given figure
We can draw this by drawing horizontal and vertical line of symmetry
Therefore,
The above given figure can be completed as follows:
(d) The above given figure can be completed by drawing the same parts as shown in the given figure
We can draw this by drawing horizontal and vertical line of symmetry
Therefore,
The above given figure can be completed as follows:
(e) The above given figure can be completed by drawing the same parts as shown in the given figure
We can draw this by drawing horizontal and vertical line of symmetry
Therefore,
The above given figure can be completed as follows:
(f) The above given figure can be completed by drawing the same parts as shown in the given figure
We can draw this by drawing horizontal and vertical line of symmetry
Therefore,
The above given figure can be completed as follows:
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 OEMNPHLTSVX
Answer:
Mirror image for above given figures is as follows:
From the above drawn figures, we have
Figures having vertical line of symmetry will have same mirror images and these are:
O, M, H, T, V, X
Thus, these letters will look the same