The idea, step by step
A mirror line matches two halves
A line of reflection symmetry divides a shape so one side would land exactly on the other if folded along that line. Both the outside shape and any decoration must match. A non-square rectangle has two mirror lines: one through the middle in each direction.
Turn the whole design
Rotational symmetry means a shape matches itself during a turn smaller than a full turn. A non-square rectangle matches after a half turn. A plain square matches after each quarter turn. Turn the whole design around its centre; moving it to another place is not the same operation.
A common trap
Any line through the centre is a line of symmetry.
Instead: A mirror line must match the full shape and its decoration, not just pass through its centre.
See the thinking
A rectangle
How many reflection lines does a plain non-square rectangle have?
- A vertical middle line matches left and right halves.
- A horizontal middle line matches top and bottom halves.
- A diagonal does not match the long sides with the short sides.
A square turn
What is the smallest turn that makes a plain square match itself?
- Turn the square about its centre.
- After a quarter turn, every side and corner fits the original outline.
Check your understanding
Does a plain non-square rectangle match itself after a quarter turn?
Show answer
No; it matches after a half turn.
A quarter turn swaps long and short directions.
Your turn
6 questions · 8 marks · Work at your own pace.
Read the questions online
- How many reflection lines does a plain square have?1 mark
- How many reflection lines does a plain non-square rectangle have?1 mark
- What is the smallest matching turn for a plain non-square rectangle?1 mark
- What is the smallest matching turn for a plain square?1 mark
- A square has a single dot near one corner. Must the decorated design keep every symmetry of the plain square?2 marks
- Explain one difference between reflection symmetry and rotational symmetry.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- How many reflection lines does a plain square have?1 mark
Two pass through side midpoints and two join opposite corners.
Four. - How many reflection lines does a plain non-square rectangle have?1 mark
Only the vertical and horizontal middle lines match the halves.
Two. - What is the smallest matching turn for a plain non-square rectangle?1 mark
Opposite sides and corners swap into matching positions.
A half turn. - What is the smallest matching turn for a plain square?1 mark
The square outline fits after each quarter turn.
A quarter turn. - A square has a single dot near one corner. Must the decorated design keep every symmetry of the plain square?2 marks
For example, a quarter turn moves the dot to a different corner.
No. The dot must match too. - Explain one difference between reflection symmetry and rotational symmetry.2 marks
Both require the entire design to match, but the movement is different.
Reflection uses a matching fold or mirror line; rotation turns the design about a centre.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics 2026
Composite shapes/objects; angle names; reflection/rotational symmetry; creating designs.
Official curriculum source ↗