NCERT Book Class 6 Maths Symmetry PDF Download

Chapter 9: Symmetry

Look around you - you may find many objects that catch your attention. Some such things are shown below:

[Figure: Flower, Butterfly, Rangoli, Pinwheel, See in your textbook]

There is something beautiful about the pictures above. The flower looks the same from many different angles. What about the butterfly? No doubt, the colours are very attractive. But what else about the butterfly appeals to you?

In these pictures, it appears that some parts of the figure are repeated and these repetitions seem to occur in a definite pattern. Can you see what repeats in the beautiful rangoli figure? In the rangoli, the red petals come back onto themselves when the flower is rotated by 90° around the centre and so do the other parts of the rangoli.

What about the pinwheel? Can you spot which pattern is repeating? Hint: Look at the hexagon first.

Now, can you say what figure repeats along each side of the hexagon? What is the shape of the figure that is stuck to each side? Do you recognise it? How do these shapes move as you move along the boundary of the hexagon? What about the other pictures - what is it about those structures that appeals to you and what are the patterns in those structures that repeat?

On the other hand, look at this picture of clouds. There is no such repetitive pattern.

[Figure: Clouds, See in your textbook]

We can say that the first four figures are symmetrical and the last one is not symmetrical. A symmetry refers to a part or parts of a figure that are repeated in some definite pattern.

[Figure: Taj Mahal and Gopuram, See in your textbook]

What are the symmetries that you see in these beautiful structures?

Teacher's Note

Symmetry is not just about mirror images - it can also be about rotation. When the rangoli rotates by 90° and looks the same, that is rotational symmetry. When you fold a shape and both halves match perfectly, that is line symmetry. Watch for both types as you explore these figures.

9.1 Line of Symmetry

Figure (a) shows the picture of a blue triangle with a dotted line. What if you fold the triangle along the dotted line? Yes, one half of the triangle covers the other half completely. These are called mirror halves!

[Figure: (a) Blue triangle with dotted line showing mirror halves, (b) Red puzzle pieces with dotted line, See in your textbook]

What about Figure (b) with the four puzzle pieces and a dotted line passing through the middle? Are they mirror halves? No, when we fold along the line, the left half does not exactly fit over the right half.

A line that cuts a figure into two parts that exactly overlap when folded along that line is called a line of symmetry of the figure.

Figure it Out

1. Do you see any line of symmetry in the figures at the start of the chapter? What about in the picture of the cloud?
2. For each of the following figures, identify the line(s) of symmetry if it exists.

[Figure: Five shapes (irregular quadrilateral, diamond, house shape, L-shape, triangle), See in your textbook]

Teacher's Note

To test if a line is a line of symmetry, imagine folding the paper along that line. If one half lands exactly on the other half with all edges and corners matching perfectly, then it is a true line of symmetry. If any part sticks out or doesn't match, it is not a line of symmetry.

Key Points

• A symmetry means that parts of a figure repeat in a definite, regular pattern.
• A line of symmetry divides a figure into two parts that are mirror halves - they match exactly when the paper is folded along that line.
• Some figures have one line of symmetry, some have many, and some have none at all.
• You can test for a line of symmetry by folding or by imagining a fold to see if both sides match perfectly.

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