Page 2 - LN 9.3

This fixed point is called the centre of rotation. Will the windmill above looks the same when rotated
through an angle of less than 90°? No!

An angle through which a figure can be rotated to look the same is called an angle of rotational
symmetry, or just an angle of symmetry, for short. For the windmill, the angles of symmetry are 90°
(quarter turn), 180° (half turn), 270° (three-quarter turn) and 360° (full turn). Observe that when any
figure is rotated by 360°, it comes back to its original position, so 360° is always an angle of
symmetry. Thus, we see that the windmill has 4 angles of symmetry.

Rotational Symmetry of Figures with Radial Arms
Consider this figure, a picture with 4 radial arms. How many angles of symmetry does it have? What
are they? Note that the angle between adjacent central dotted lines is 90° and the figure has 4 angles
of symmetry.

Symmetries of a Circle
The circle is a fascinating figure. What happens when you rotate a circle clockwise about its center?
It coincides with itself. It does not matter what angle you rotate it by! So, for a circle, every angle is
an angle of symmetry.

Now take a point on the rim of the circle and join it to the centre. Extend the segment to the diameter
of the circle. Is that diameter a line of reflection symmetry? It is. Every diameter is a line of
symmetry! Like wheels, we can find other objects around us having rotational symmetry. Find them.