Line Symmetry and Rotational Symmetry

You have been observing many shapes and their symmetries so far. By now you would have understood that some shapes have only line symmetry, some have only rotational symmetry and some have both line symmetry and rotational symmetry.

For example, consider the square shape .

How many lines of symmetry does it have?

Before that let we mark the of the sides of square.

Now draw the lines of symmetry

Therefore it has lines of symmetry

Does it have any rotational symmetry?

If ‘yes’, what is the order of the rotational symmetry?

Therefore, it has order 4 of rotational symmetry.

The circle is the most perfect symmetrical figure, because it can be rotated around its through any angle and at the same time it has unlimited number of lines of symmetry. Observe any circle pattern.

Every line through the centre (that is every diameter) forms a line of (reflectional) symmetry and it has rotational symmetry around the centre for every angle.

Some of the English alphabets have fascinating symmetrical structures.Which capital letters have just one line of symmetry (like E)? Which capital letters have a rotational symmetry of order 2 (like I)?

Line Symmetry Order = 0, Rotational Symmetry Order = 1

Line Symmetry Order = 0, Rotational Symmetry Order = 2

Line Symmetry Order = 1, Rotational Symmetry Order = 1

Line Symmetry Order = 2, Rotational Symmetry Order = 2

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Line Symmetry and Rotational Symmetry