Angles and Symmetry
Line and Rotational Symmetry

An object has rotational symmetry if it can be rotated about a point so that it fits on top of itself without completing a full turn. The shapes below have rotational symmetry.

In a complete turn this shape fits on top of itself two times.

It has rotational symmetry of order 2.

In a complete turn this shape fits on top of itself four times.

It has rotational symmetry of order 4.

Shapes have line symmetry if a mirror could be placed so that one side is an exact reflection of the other. These imaginary 'mirror lines' are shown by dotted lines in the diagrams below.

This shape has 2 lines of symmetry.

This shape has 4 lines of symmetry.

Worked Examples

1

For the given shape, state:

(a)

the number of lines of symmetry,

Show me

There are 3 lines of symmetry as shown.
(b)

the order of rotational symmetry.

Show me

There is rotational symmetry with order 3, because the point marked A could be rotated to A' then to A'' and fit exactly over its original shape at each of these points.

Exercises

For each shape below state:

how many lines of symmetry it has if there is any;

the order of symmetry if it has rotational symmetry.

Leave blank the input box if no input needed.

(a)

symmetry lines:

order =

(b)

symmetry lines:

order =

(c)

symmetry lines:

order =

(d)

symmetry lines:

order =

(e)

symmetry lines:

order =

(f)

symmetry lines:

order =

(g)

symmetry lines:

order =

(h)

symmetry lines:

order =

(i)

symmetry lines:

order =

For each shape below state:

how many lines of symmetry it has if there is any;

the order of symmetry if it has rotational symmetry.

Leave blank the input box if no input needed.

(a)

symmetry lines:

order =

(b)

symmetry lines:

order =

(c)

symmetry lines:

order =

(d)

symmetry lines:

order =

(e)

symmetry lines:

order =

(f)

symmetry lines:

order =

(g)

symmetry lines:

order =

(h)

symmetry lines:

order =

(i)

symmetry lines:

order =

Is it possible to draw:

(a)

a pentagon with exactly 2 lines of symmetry,

(b)

a hexagon with exactly 2 lines of symmetry,

(c)

an octagon with exactly 3 lines of symmetry?

These are the initials of the International Association of Whistlers.

I A W

Which of these letters has rotational symmetry?

Which of the designs below have line symmetry?