Maths

Symmetry

Reflection symmetry

A shape is symmetrical if both sides of it are the same when a mirror line is drawn.

What happens when you fold this shape? Choose a fold line to find out.

If you stood a mirror on this shape and looked at it from each side, what would you see?

Choose a mirror line to find out.

This shape is symmetrical. It has reflection symmetry. It has one line of symmetry.

When you fold a shape along a line of symmetry, one half fits exactly over the other.

When you put a mirror on a line of symmetry and look from either side, the shape looks like the original.

Remember

When you look in a mirror you see your reflection. So it is easy to remember that when a shape has a line of symmetry it has reflection symmetry.

  • Line of symmetry: a mirror or fold line.
  • Reflection symmetry: when there are one or more lines of symmetry.

More lines of symmetry

Some shapes have several lines of symmetry. How many lines of symmetry does a square have?

Check to see if you were right.

Remember a square has 4 lines of symmetry, not 8. Be careful to only count each line once!

Now try to work out how many lines of symmetry these shapes have.

It is easy to get caught out with some shapes.

Are these lines of symmetry? First, try to figure out what you would see in a mirror on each line. Then check to see if you were right.

Now that you have looked at some examples, you should be feeling confident enough to attempt a question yourself.

Question

How many lines of symmetry does this shape have?

images: parallelogram

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Answer

This is a parallelogram. It is easy to get caught out with parallelograms, because they do not have any lines of symmetry. Parallelograms do not have reflection symmetry.

If you are not sure about a line of symmetry, you could:

  • sketch the shape on a rough piece paper and fold it to see what happens, or
  • use a mirror to test the line

Rotation symmetry

A tracing of this shape fits the shape exactly in 4 different ways.

The number of different ways in which the tracing fits is the order of rotation symmetry. This shape has rotation symmetry of order 4.

Remember:

If a shape will only fit itself in one way, it has no rotation symmetry. Because it fits in only one way, it has rotation symmetry of order 1!

For each shape below, decide whether it has rotation symmetry, decide on the order, and where the centre is. Then check to see if you were right.

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