NCERT Solutions For Class 6 Maths Chapter 13 Exercise 13.3
Ncert Solutions for Class 6 Maths Chapter 13 Symmetry Exercise 13.3:-
Exercise 13.3 Class 6 maths NCERT solutions Chapter 13 Symmetry pdf download:-
Ncert Solution for Class 6 Maths Chapter 13 Symmetry Exercise 13.3 Tips:-
Introduction:-
Reflection and Symmetry
Line symmetry and mirror reflection are naturally related and linked to each
other.
Here is a picture showing the reflection of the English letter M. You can
imagine that the mirror is invisible and can just see the letter M and its image.
The object and its image are symmetrical with reference
to the mirror line. If the paper is folded, the mirror line
becomes the line of symmetry. We then say that the image is
the reflection of the object in the mirror line. You can also
see that when an object is reflected, there is no change in the
lengths and angles; i.e. the lengths and angles of the object
and the corresponding lengths and angles of the image are
the same. However, in one aspect there is a change, i.e. there
is a difference between the object and the image. Can you
guess what the difference is?
(Hint : Look yourself into a mirror).
On a squared sheet, draw the figure ABC and find its
mirror image A’B’C’ with l as the mirror line.
Compare the lengths of
AB and A’B’; BC and B’C’; AC and A’C’.
Are they different?
Does reflection change length of a line segment?
Compare the measures of the angles (use protractor
to measure) ABC and A’B’C’.
Does reflection change the size of an angle?
Join AA’, BB’ and CC’. Use your protractor to measure the angles between
the lines l and AA’, l and BB’, l and CC’.
What do you conclude about the angle between the mirror line l and the
line segment joining a point and its reflected image?
Paper decoration
Use thin rectangular
coloured paper. Fold it
several times and create
some intricate patterns by
cutting the paper, like the
one shown here. Identify
the line symmetries in the
repeating design. Use such
decorative paper cut-outs
for festive occasions.
Do This
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?
Kaleidoscope
A kaleidoscope uses mirrors to produce
images that have several lines of
symmetry (as shown here for example).
Usually, two mirrors strips forming a V-
shape are used. The angle between the
mirrors determines the number of lines
of symmetry.
Make a kaleidoscope and try to learn more about the symmetric images
produced.
Album
Collect symmetrical designs you come across and prepare an album.
Here are a few samples.
An application of reflectional symmetry
A paper-delivery boy wants to park his cycle at
some point P and deliver the newspapers to
houses A and B. Where should he park the cycle
so that his walking distance AP + BP will be least?
You can use reflectional symmetry here. Let
A’ be the image of A in the mirror line which is
the street here. Then the point P is the ideal place
to park the cycle (where the mirror line and A’B
meet). Can you say why?
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