Maths Chapter 12: Symmetry

A figure has line symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.

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.

Mirror reflection leads to symmetry, under which the left-right orientation have to be taken care of.

Rotation turns an object about a fixed point. This fixed point is the centre of rotation. The angle by which the object rotates is the angle of rotation. 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 a 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. The order of symmetry of a square, for example, is 4 while, for an equilateral triangle, it is 3.

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.