### Symmetry - Revision Notes

CBSE Class–VII Subject Mathematics

Revision Notes
Chapter –14
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.
 Regular Polygon Regular hexagon Regular pentagon Square Equilateral triangle Number of lines of symmetry 6 5 4 3
• 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 ${180}^{0}$  ; a quarter-turn means rotation by ${90}^{0}$ .  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 ${360}^{0}$ ), 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. 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.