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SAI International School
CLASS – VII, SUB: MATH

CHAPTER 14: SYMMETRY

Lesson Notes - 2

TOPIC: ROTATIONAL SYMMETRY

SUBTOPIC: Centre of Rotation, Angle of rotation, Order of symmetry

LESSON NOTES:Rotation, like movement of the hands of a clock, is called
a clockwise rotation; otherwise it is said to be anticlockwise.

Rotational Symmetry: If a figure is rotated around a centre point and it still appears
exactly as it did before the rotation, it is said to have rotational symmetry.

 A number of shapes like squares, circles, regular hexagon, etc. have
rotational symmetry.
 There are many shapes you will see in geometry which are symmetrical
rotationally, such as:
o Equilateral triangles
o Squares
o Rectangles
o Circles
o Regular Polygons

Centre of Rotation:For a figure or object that has rotational symmetry, the fixed
point around which the rotation occurs is called the centre of rotation.
 Ex- The centre of rotation of a windmill in the centre of the windmill from which
its blades originate.

Angle of Rotational Symmetry: For a figure or object that has rotational symmetry,
the angle of turning during rotation is called the angle of rotation.
 Ex- When a square is rotated by 90 degrees, it appears the same after
rotation. So, the angle of rotation for a square is 90 degrees.
 In the same way, a regular hexagon has an angle of symmetry as 60
degrees; a regular pentagon has 72 degrees, and so on.

Order of Rotational Symmetry: The number of positions in which a figure can be
rotated and still appears exactly as it did before the rotation, is called the order of
symmetry.
 For example, a star can be rotated 5 times along its tip and look at the same
every time. Hence, its order of symmetry is 5.
 If we consider the order of symmetry for regular hexagon it is equal to 6, since
it has 6 equal sides and is rotated with an angle of 60 degrees.