Understand the idea.
A mirror line matches two halves
A line of reflection symmetry is a fold line that makes the whole design match exactly. Corresponding points lie equal distances on opposite sides of the line. Check the outline and every colour or decoration, not just the overall balance.
A plain non-square rectangle has a vertical and a horizontal line through its centre. Folding along either matches the two halves. A centre line is only a symmetry line when the matching test succeeds.
Turn the whole design
For rotational symmetry, turn the whole shape around a fixed centre. It must match its original position after a turn smaller than a full turn. A plain square matches after a quarter turn; a non-square rectangle first matches after a half turn.
Keep the centre fixed rather than sliding the shape into place. Decorations must move onto identical decorations. A plain outline may have symmetry that disappears when a dot or colour is added in only one place.
See the method in action.
A rectangle
How many reflection lines does a plain non-square rectangle have?
Worked solution
- 1
Test the vertical centre line.
Folding left to right matches the rectangle’s equal halves, so this is one reflection line.
- 2
Test the horizontal centre line.
Folding top to bottom also matches the outline, giving a second line.
- 3
Check the diagonals.
In a non-square rectangle a diagonal fold would not match long and short edges, so neither diagonal is a reflection line.
- 4
Count the successful lines.
Only the vertical and horizontal centre lines match the complete rectangle.
Two reflection lines.
A square turn
What is the smallest turn that makes a plain square match itself?
Worked solution
- 1
Keep the centre of the square fixed.
Rotational symmetry is tested by turning about the centre without sliding the shape.
- 2
Turn to the next matching side.
The square has four equal sides and right-angle corners, so a quarter turn moves each side onto the next.
- 3
Check that this is the smallest positive matching turn.
A smaller positive turn leaves the side directions different; the quarter turn is the first time all sides and corners match.
A quarter turn.
Try it yourself.
Check your understanding
Does a plain non-square rectangle match itself after a quarter turn?
Show answer & reasoning
No; it matches after a half turn.
No. A quarter turn changes the rectangle’s long direction into its short direction, so the outline does not match. A half turn puts long sides and short sides back onto matching sides.
Keep practising
6 worksheet questions · 8 marks
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 ↗