Class
6 Maths NCERT Solutions
Chapter
13 Symmetry
Exercise 13.1
Q.1: List any four symmetrical objects from
your home or school.
Ans : Paper sheet, Glass, CD, Bucket
Q.2: For the given figure, which one is the
mirror line, 
?
Ans : Line l2 is the mirror
line of this figure. This is because when the given figure is folded about the
line l2, the left part can exactly cover the right part
and vice-versa.
Q.3: Identify the shapes given below. Check
whether they are symmetric or not. Draw the line of symmetry as well.
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(a) |
(b) |
(c) |
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(d) |
(e) |
(f) |
Ans :
(a) Yes
(b) Yes
(c) No
(d) Yes
(e) Yes
(f) Yes
Line of symmetry is shown in the following figures.
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(a) |
(b) |
(d) |
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(e) |
(f) |
Q.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.
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(a) |
(b) |
(c) |
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(d) |
(e) |
(f) |
Ans :
To make the dotted line as the line of symmetry,
the given figures can be drawn as follows.
(a)
(b)
(c)
(d)
(e)
(f)
Q.5: In the figure, l is
the line of symmetry.
Complete the diagram to make it symmetric.
Ans :
To make the diagram symmetric, it can be completed
as follows.
Q.6: In figure, l is the
line of symmetry.
Draw the image of the triangle and complete the
diagram so that it becomes symmetric.
Ans :
The required triangle can be formed as follows.
Exercise 13.2
Q.1: Find the number of lines of symmetry
for each of the following shapes:
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(a) |
(b) |
(c) |
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(d) |
(e) |
(f) |
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(g) |
(h) |
(i) |
Ans :
(a) There are 4 lines of symmetry for
the given figure.
(b) There are 4 lines of symmetry for
the given figure.
(c) There are 4 lines of symmetry for
the given figure.
(d) There is only 1 line of symmetry
for the given figure.
(e) There are 6 lines of symmetry for
the given figure.
(f) There are 6 lines of symmetry for
the given figure.
(g) There is no line of symmetry for
the given figure.
(h) There is no line of symmetry for
the given figure.
(i) There are 3 lines of symmetry for
the given figure.
The lines of symmetry in the above figures can be
represented as follows.
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(a) |
(b) |
(c) |
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(d) |
(e) |
(f) |
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(i) |
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Q.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!)
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(a) |
(b) |
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(c) |
(d) |
Ans :
(a) It is an isosceles triangle. There will be only
1 line of symmetry.
(b) It is an isosceles triangle. There will be only
1 line of symmetry.
(c) It is a right-angled triangle. There will be
only 1 line of symmetry.
(d) It is a scalene triangle. There will be no line
of symmetry.
Q.3: Complete the following table.
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Shape |
Rough
figure |
Number of
lines of symmetry |
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Equilateral
triangle |
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3 |
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Square |
- |
- |
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Rectangle |
- |
- |
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Isosceles
triangle |
- |
- |
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Rhombus |
- |
- |
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Circle |
- |
- |
Ans :
The given table can be completed as follows.
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Shape |
Rough
figure |
Number of
lines of symmetry |
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Equilateral
triangle |
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3 |
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Square |
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4 |
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Rectangle |
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2 |
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Isosceles
triangle |
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1 |
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Rhombus |
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2 |
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Circle |
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Infinite |
In case of a circle, there are infinite lines. In
the above table, only some lines of symmetry are drawn. More symmetric lines
can be similarly drawn for it.
Q.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.
Ans :
(a) Yes, we can make an isosceles triangle which
has 1 line of symmetry.
(b) No, we cannot draw such a triangle.
(c) Yes, we can make an equilateral triangle which
has 3 lines of symmetry.
(d) Yes, we can make a scalene triangle which has
no line of symmetry.
Q.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.)
Ans :
(a) A triangle with only 1 horizontal line of
symmetry and no other vertical line of symmetry can be sketched as follows.
(b) A quadrilateral with both horizontal and
vertical lines of symmetry
can be drawn as follows.
(c) A quadrilateral with a horizontal line of
symmetry but no vertical line of symmetry can be drawn as follows.
(d) A hexagon with exactly two lines of symmetry
can be sketched as follows.
(e) A hexagon with six lines of symmetry can be
sketched as follows.
Q.6: Trace each figure and draw the lines of
symmetry, if any:
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(a) |
(b) |
(c) |
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(d) |
(e) |
(f) |
Ans :
(a) The given figure is an isosceles triangle.
Therefore, there will be 1 line
of symmetry.
(b) The given figure has 2 lines of symmetry.
(c) The given figure has 4 lines of symmetry.
(d) The given figure is an octagonal having 2 lines
of symmetry.
(e) The given figure has only 1 line of symmetry.
(f) The given figure has 4 lines of symmetry.
Q.7: Consider the letters of English
alphabet, 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)
Ans :
(a) A, H, I, M, O, T, U, V, W, X, Y
(b) B, C, D, E, H, I, K, O, X
(c) F, G, J, L, N, P, Q, R, S, Z
Q.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.
Ans :
The complete figures will be as follows.
Exercise 13.3
Q.1: Find the number of lines of symmetry in
each of the following shapes. How will you check your answers?
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(a) |
(b) |
(c) |
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(d) |
(e) |
(f) |
Ans :
(a) It can be observed that there are 4 lines of
symmetry.
(b) It can be observed that there is only 1 line of
symmetry.
(c) It can be observed that there are 2 lines of
symmetry.
(d) It can be observed that there are 2 lines of
symmetry.
(e) It can be observed that there is only 1 line of
symmetry.
(f) It can be observed that there are 2 lines of
symmetry.
Q.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?
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(a) |
(b) |
(c) |
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(d) |
(e) |
(f) |
Ans :
These figures can be completed by drawing similar
parts as shown in these figures, first about the vertical line of symmetry and
then about the horizontal line of symmetry, or first about the horizontal line
of symmetry and then about the vertical line of symmetry.
The completed figures will be as follows.
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(a) |
(b) |
(c) |
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(d) |
(e) |
(f) |
Q.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
Ans :
The mirror images of these figures will be as
follows.
The letters that have vertical line of symmetry
will have same mirror images. These letters are O, M, H, T, V, X and hence,
these letters will look the same.
End of Questions