Symmetry

A regular polygon has all the sides equal and also all the interior angles are of equal measure.

The linear symmetry is a symmetry in which a line divides a given figure into two identical halves, then the given figure has line symmetry. The line is called the axis of symmetry or line of symmetry.

An equilateral triangle has three lines of symmetry. A regular pentagon has five lines of symmetry. A square has four lines of symmetry. A regular hexagon has six lines of symmetry. Regular polygons have multiple lines of symmetry.

A shape has line symmetry when one half of it is the mirror image of the other half. When dealing with mirror reflection, the left-right changes in orientation are taken into account.

If an object can be rotated through a certain angle about a fixed point so that the image is identical to its initial position, then the figure has rotational symmetry. Clockwise and anticlockwise are the two types of rotation. The point around which the object rotates is called the centre of rotation. The angle by which the object rotates is called the angle of rotation. Angle of rotation for a quarter turn is 90°. Angle of rotation for a half turn is 180°. Angle of rotation for a full turn is 360°. Order of rotational symmetry is the number of times an object looks exactly the same in a complete turn of 360 degrees. If an object matches its original appearance only once in a full 360° rotation then the object does not have rotational symmetry and the order of symmetry is 1.

Some shapes have only one line of symmetry, some have only rotational symmetry, and some shapes have both symmetries.

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