Math's holiday homework

symmetry

INTRODUCTION Symmetry generally conveys two

primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection. The second meaning is a precise and well-defined concept of balance or "patterned self-similarity" that can be demonstrated or proved according to the rules of a formal system: by geometry, through physics or otherwise.

LINES OF SYMMETRY

FOR REGULAR POLYGON

An equilateral triangle is regular because each of its sides has same lengths and each of its angles measure 60°.

A square is also regular because all its sides are of equal lengths and each of its angle is a right angle (i.e.90 °). Its diagonals are seem to be perpendicular bisectors of one another.

If pentagon is regular, naturally, its sides should have equal length. Measure of each of its angle is 108°.

A regular hexagon has all its sides equal and each of its angles measures 120°.

LINES OF SYMMETRY

Triangle Square Pentagon Hexagon 3 lines of 4 lines of 5 lines of 6 lines of Symmetry Symmetry Symmetry Symmetry

Points to remember Any object or shape is said to have rotational symmetry if it

looks exactly the same at least once during a complete rotation through three hundred and sixty degrees.

During the rotation, the object rotates around a fixed point. Its shape and size do not change.

This fixed point is called the centre of rotation. Rotation may be clockwise or anti-clockwise. A full turn refers to a rotation of three hundred and sixty

degrees. A half turn refers to a rotation of one hundred and eighty

degrees. A quarter turn refers to a rotation of ninety degrees. The angle at which a shape or an object looks exactly the same

during rotation is called the angle of rotation. The order of rotational symmetry can be defined as the

number of times that a shape appears exactly the same during a full 360orotation.

ROTATIONAL SYMMETRY

When an object rotates, its shapes and size do not change. The rotation turns an object about a fixed point. This fixed point is the centre of the rotation.

The angle of turning during rotation is called angle of rotation. A full turn is 360o.

• Half turn means rotation by 180 °.

A quarter turn is rotation by 90 °.

WHICH LETTERS HAVROTATIONAL SYMMETRY?

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H I N OS X Z

WHICH ROAD SIGNS HAVE GOT ROTAIONAL SYMMETRY? •

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Oh! I lost count…

Order 2

Order3

Order2

Made by-Samyak Jain