ROTATIONAL SYMMETRY Highlights of Presentaton: Order of rotational symmetry Centre of rotational symmetry Angle of rotational symmetry Examples of shapes Presented by: JYOTI SINGH TGT Maths KV Mughalsarai (Varanasi region)

Rotational Symmetry An object is said to possess rotational symmetry when it looks exactly the same after a rotation. The degree of rotational symmetry that an object has is known as its order. The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees. Rotation turns the object about a fixed point which is know as centre of rotation. PowerPoint XP or above is needed to view the rotations on this presentation. During rotation the angle at which the object attains its original shape is called angle of rotation.

Rotational Symmetry For shapes that have only “order 1” rotational symmetry a centre of rotation can be found anywhere within it. For shapes that have “order 2” rotational symmetry or higher, a single centre of rotation can be located. PowerPoint XP or above is needed to view the rotations on this presentation. Order 1 Order 2 Order 3 Order 4

Rotational Symmetry The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees. Order 1

Rotational Symmetry The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees. 2 1 Order 1 Order 2

Rotational Symmetry The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees. 2 1 Order 1 Order 2 3 2 1 Order 3

Rotational Symmetry The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees. 2 1 Order 1 Order 2 3 3 4 2 1 2 1 Order 4 Order 3

Rotational Symmetry The figure attains its original shape at every turn of 120 degrees.This is the angle of rotation for given figure. 3 120 degrees turn 120 degrees turn 2 1 120 degrees turn Order 3

Rotational Symmetry This figure attains its original shape four times during the complete rotation each at an angle of 90 degrees .Angle of rotation is 90 degrees. 90 degrees turn 90 degrees turn 3 4 2 1 90 degrees turn 90 degrees turn Order 4

NOW EXAMPLES OF ROTATIONAL SYMMETRY FOR POLYGONS

Regular Polygons Equilateral Triangle An equilateral triangle has rotational symmetry of order ? Regular Polygons

Equilateral Triangle An equilateral triangle has rotational symmetry of order ?

Equilateral Triangle An equilateral triangle has rotational symmetry of order ? 3 3 2 1

Square A square has rotational symmetry of order ? Square

Square A square has rotational symmetry of order ?

Square A square has rotational symmetry of order ? 4 3 4 2 1

Pentagon Regular Pentagon A regular pentagon has rotational symmetry of order ? Pentagon

Regular Pentagon A regular pentagon has rotational symmetry of order ?

Regular Pentagon A regular pentagon has rotational symmetry of order ? 5 5 4 1 3 2

Hexagon Regular Hexagon A regular hexagon has rotational symmetry of order ? Hexagon

Regular Hexagon A regular hexagon has rotational symmetry of order ?

Regular Hexagon 6 A regular hexagon has rotational symmetry of order ? 5 6 4 1 3 2

Octagon Regular Octagon A regular octagon has rotational symmetry of order ? Octagon

Regular Octagon 8 A regular octagon has rotational symmetry of order ? 7 8 6 1 5 2 4 3

Rectangle A rectangle has rotational symmetry of order ? Rectangle

Rectangle A rectangle has rotational symmetry of order ? 2 2 1

Parallelogram A parallelogram has rotational symmetry of order ?

Parallelogram 2 A parallelogram has rotational symmetry of order ? 2 1

Isosceles Triangle An isosceles triangle has rotational symmetry of order ?

Isosceles Triangle 1 An isosceles triangle has rotational symmetry of order ? 1

Scalene Triangle An scalene triangle has rotational symmetry of order ?

Scalene Triangle 1 An scalene triangle has rotational symmetry of order ? 1

Isosceles Trapezium An isosceles trapezium has rotational symmetry of order ?

Isosceles Trapezium An isosceles trapezium has rotational symmetry of order ? 1 1

Trapezium A trapezium has rotational symmetry of order ?

Trapezium 1 A trapezium has rotational symmetry of order ? 1

Kite A kite has rotational symmetry of order ?

Kite 1 A kite has rotational symmetry of order ? 1

Rhombus A rhombus has rotational symmetry of order ?

Rhombus 2 A rhombus has rotational symmetry of order ? 2 1

Questions 1 Rotational Symmetry State the order of rotational symmetry for each shape below: 1 2 3 4 Order 6 Order 2 Order 3 Order 2 5 6 7 8 Order 1 Order 3 Order 2 Order 5 9 10 11 12 Questions 1 Order 4 Order 1 Order 6 Order 8