MATHEMATICSRotational Symmetry

Lesson Objectives

•The aim of this powerpoint is to help you…

• Find the order of rotational symmetry

• Draw rotationally symmetric shapes

Remember…

• Symmetry is the quality of being made up of exactly similar parts either facing each other (as in reflective symmetry) or around an axis (as in rotational symmetry).

• We have already looked at line symmetry – with mirror lines and mirror images.

• Now we are looking at rotational symmetry which involves turning.

Order of Rotational Symmetry• When you turn an object (about its centre point) through 1

full turn (i.e. 360°), the number of times it looks identical to its starting position is its order of symmetry.

• [Using tracing paper helps!]

• ALL objects look exactly the same as the start after 1 full turn so ALL objects have an order of at least 1!

• Objects are only rotationally symmetric IF their order of rotational symmetry is bigger than 1.

Order of Rotational Symmetry• Here is a shape. • What order of rotational symmetry does it have?

Finding the Order of Rotation

• Let’s turn it through 360° and see how many times it looks exactly as it did at the start:

Turning clockwise through 360°

• After 180° and 360° it looked exactly the same. • A parallelogram has rotational symmetry of order 2.

P P

Order of Rotational Symmetry• Here is a shape. • What order of rotational symmetry does it have?

Finding the Order of Rotation

• Let’s turn it through 360° and see how many times it looks exactly as it did at the start:

Turning clockwise through 360°

• After 90°, 180°, 270° and 360° it looked exactly the same.

• This cross has rotational symmetry of order 4.

P P PP

Order of Rotational Symmetry• Here are 2 road signs. • The one on the left has rotational symmetry order 3.• The one on the right has rotational symmetry order 1.• Can you explain why?

Order of Rotational Symmetry• Let’s rotate both road signs…

After 120° After 240° After 360°

Order 3

Order 1

P

P

PP

O O

Small Group Task• Please get into 2 groups.• Each group will be given a different set of signs.• TOGETHER, discuss and decide what order of symmetry

each sign has.

• Once complete, designate one person in your group to present your solution to the other group.

• The solutions will appear on the next two slides so do NOT move on until after your presentations.

Rotational Symmetry – Set 1

A C E G I

K L O Q S

U W Z

Rotational Symmetry – Set 2

B D F H J

M N P R T

V X Y

Drawing rotationally symmetric shapes

• Decide what order of rotational symmetry you wish to design.

• Divide 360° by this value.

• Draw a vertical line about a point. Measure your angle and then draw another line the same length as the first one.

• Repeat the above starting from your new line, until you have gone all the way around the point.

• Design your outside shape and then fill-in the same design in each section.

I’d like rotational symmetry of order 5 so…

360° ÷ 5 = 72°

72°72°

72°72°72°

Notes and Examples• In your exercise books or on paper, please write up your

own notes and examples on rotational symmetry.• It may help to include answers to the following

questions…1) How do you work out the order of rotational symmetry?

2) How can you draw a rotationally symmetric shape or design?

What next?Ask your teacher for the instructions and templates for…

a) Designing your own reflectively symmetric pattern/shape

b) Designing your own rotationally symmetric pattern/shape