Chapter -14

Symmetry

Symmetry comes from a Greek word meaning 'to measure together'

If two or more parts of a figure are identical after folding, then it is said to be symmetry. An image is said to be symmetrical when two halves of an image are of same shape and size.

Line of symmetry:

An imaginary line divides a figure into two equal halves, and the line is called a line of symmetry or axis of symmetry.

> Line of symmetry can be horizontal, vertical or diagonal.

> There can be one or more lines of symmetry in a figure

When an image is observed by placing a mirror beside it, we can see the reflection of the image on the mirror, and we observe that the reflected image is the same as the original, this is called reflection symmetry.

The black surface is acting as a mirror, and we observe the reflection of shapes on the mirror, which are symmetric along the mirror surface. This mirror surface is called the mirror line along which the shapes are reflecting and showing symmetry.

We can see reflection symmetry in nature along the side of water bodies (Figure - 2), here we observe the reflection of the building and trees caused on the surface of the water.

In simple terms, we can say symmetry caused by one (or) half of an object is a mirror image of the other.

When an object (or) shape is rotated around its central point, it looks the same. The rotation can be a complete rotation or a partial rotation with some angle. This concept is called rotation symmetry.

We can observe rotational symmetry around us in many objects like ceiling fans, windmill, wheel etc.

To understand the concept of rotation, we here have a simple example to understand better hands of a clock.

• We know that the hands of a clock rotate only in one direction and along with a fixed point. This fixed point is the center of the clock.
• This movement of rotation of the hands of a clock is called clockwise rotation.
• When an object rotates in opposite orientation to the hands of a clock, this movement is called anti-clockwise rotation.

When an object shows rotational symmetry, it rotates around its center in an angle. The angle by which the object is turned once is called its angle of rotation. For one complete rotation, an object has to turn 360°.

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