**Symmetry**

- Symmetry is a geometrical concept that is found in most cases including nature.
- Any geometric shape can be said to be symmetric or asymmetric
- A shape is said to be symmetric if there exists an imaginary line passing through that divides the shape into halves and that these halves overlap each other completely.
- In other words, fold the shape about the imaginary line to check if the two halves completely overlap each other or not. If they overlap each other completely the shape is symmetric, if not, then it is asymmetric.
- The imaginary line is called as the
**line of symmetry**. - The symmetry observed in the above example is called as a line or bilateral symmetry.

A half-turn means rotation by 180°; a quarter-turn means rotation by 90°.

Rotation may be clockwise or anticlockwise.

If, after a rotation, an object looks exactly the same, we say that it has rotational symmetry.

In a complete turn (of 360°), the number of times an object looks exactly the same is called the order of rotational symmetry. For example, the order of symmetry of a square is 4 while, for an equilateral triangle, it is 3.

**Line Symmetry and Rotational Symmetry**

Some shapes have only one line of symmetry, like the letter E;

Some have only rotational symmetry, like the letter S;

and some have both symmetries like the letter H.

The study of symmetry is important because of its frequent use in day-to-day life and more because of the beautiful designs it can provide us.

A figure is said to be symmetrical about a line l if it is identical on either side of l. In the adjoining figure, / is the line of symmetry or axis of symmetry.

Regular polygons have equal sides and equal angles. They have multiple (i.e. more than one) lines of symmetry.

Each regular polygon has as many lines of symmetry as it has sides.

**Lines of Symmetry of some Irregular Polygons.**

Each of the following capital letters of the English alphabet is symmetrical about the dotted line or lines as shown:

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