# 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?