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.

During rotation the angle at which the object attains its original shape is called angle of rotation.

Rotation turns the object about a fixed point which is know as centre of rotation.

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.

Rotational Symmetry

Order 1 Order 2 Order 3 Order 4

For shapes that have “order 2” rotational symmetry or higher, a single centre of rotation can be located.

For shapes that have only “order 1” rotational symmetry a centre of rotation can be found anywhere within it.

Rotational SymmetryThe 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

Order 11

2

Order 2

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.

Rotational Symmetry

Order 11

2

Order 2

12

3

Order 3

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.

Rotational Symmetry

Order 11

2

Order 2

12

3

Order 312

3 4

Order 4

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.

Rotational Symmetry

12

3

Order 3

The figure attains its original shape at every turn of 120 degrees.This is the angle of rotation for given figure.

120 degrees turn

120 degrees turn

120 degrees turn

Rotational Symmetry

12

3 4

Order 4

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

90 degrees turn

90 degrees turn

NOW EXAMPLES OF ROTATIONAL SYMMETRY FOR POLYGONS

Equilateral Triangle

An equilateral triangle has rotational symmetry of order ?

Regular PolygonsRegular Polygons

Equilateral Triangle

An equilateral triangle has rotational symmetry of order ?

Equilateral Triangle

An equilateral triangle has rotational symmetry of order ?

12

33

Square

A square has rotational symmetry of order ?

SquareSquare

Square

A square has rotational symmetry of order ?

Square

A square has rotational symmetry of order ?

12

3

4

4

PentagonPentagon

Regular Pentagon

A regular pentagon has rotational symmetry of order ?

Regular Pentagon

A regular pentagon has rotational symmetry of order ?

Regular Pentagon

A regular pentagon has rotational symmetry of order ? 5

1

23

4

5

HexagonHexagon

Regular HexagonA regular hexagon has rotational symmetry of order ?

Regular HexagonA regular hexagon has rotational symmetry of order ?

1

23

4

5 6

Regular HexagonA regular hexagon has rotational symmetry of order ? 6

Regular OctagonA regular octagon has rotational symmetry of order ?

OctagonOctagon

1

2

34

5

6

Regular OctagonA regular octagon has rotational symmetry of order ? 8

7 8

RectangleRectangle

RectangleA rectangle has rotational symmetry of order ?

2

1

2

RectangleA rectangle has rotational symmetry of order ?

ParallelogramA parallelogram has rotational symmetry of order ?

2

1

2

ParallelogramA parallelogram has rotational symmetry of order ?

Isosceles TriangleAn isosceles triangle has rotational symmetry of order ?

1

1

Isosceles TriangleAn isosceles triangle has rotational symmetry of order ?

Scalene TriangleAn scalene triangle has rotational symmetry of order ?

1

1

Scalene TriangleAn scalene triangle has rotational symmetry of order ?

Isosceles TrapeziumAn isosceles trapezium has rotational symmetry of order ?

1

1

Isosceles TrapeziumAn isosceles trapezium has rotational symmetry of order ?

TrapeziumA trapezium has rotational symmetry of order ?

1

1

A trapezium has rotational symmetry of order ?

Trapezium

A kite has rotational symmetry of order ?

Kite

1

1

A kite has rotational symmetry of order ?

Kite

A rhombus has rotational symmetry of order ?

Rhombus

2

1

A rhombus has rotational symmetry of order ?

Rhombus

2

Questions 1Questions 1

Rotational SymmetryState the order of rotational symmetry for each shape below:

1 2 3 4

5 6 7 8

9 10 11 12

Order 6 Order 2 Order 3 Order 2

Order 1 Order 3 Order 2 Order 5

Order 4 Order 1 Order 6 Order 8