The idea, step by step
A mirror line matches the whole shape
A line of symmetry reflects the whole shape onto itself. Imagine folding along it: every part must match its reflected partner. A square has four lines of symmetry: two through opposite side midpoints and two diagonals.
A rectangle that is not a square has two lines of symmetry, not four. Its diagonals do not fold the long sides onto the short sides.
Turn the outline onto itself
A shape has rotational symmetry when a turn smaller than a full turn makes it look unchanged. A non-square rectangle matches after a half turn. A square matches after each quarter turn.
Mark a suitable centre and compare the whole outline after turning. Matching just one corner is not enough. Reflection and rotation are different transformations, even when both can map a shape onto itself.
A common trap
Any line that divides an area in half is a symmetry line.
Instead: Equal area is not enough. Reflection must match corresponding points and the whole outline.
See the thinking
Test a proposed symmetry line
A triangle has vertices A(1,1), B(5,1), C(3,5). Is x = 3 a symmetry line?
- A and B are equally far from x = 3 on opposite sides.
- C lies on the line, while the two equal sides exchange places.
Compare two turns
A non-square rectangle matches after a half turn. Must a quarter turn also match?
- A quarter turn swaps the long and short directions.
- Their unequal lengths prevent the outline from matching.
Check your understanding
How many lines of symmetry does a square have?
Show answer
4
Two join opposite side midpoints; two join opposite vertices.
Your turn
6 questions · 9 marks · Work at your own pace.
Read the questions online
- How many lines of symmetry does a non-square rectangle have?1 mark
- Does a square match itself after a quarter turn about its centre?1 mark
- Does a non-square rectangle match itself after a half turn about its centre?1 mark
- A shape is symmetric across x = 3. One vertex is at (1, 4). Where is its matching vertex?2 marks
- An isosceles triangle has two equal sloping sides and a different-length base. Describe its one line of symmetry.2 marks
- Leah calls the diagonal of a non-square rectangle a mirror line because it cuts the area in half. Explain the mistake.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- How many lines of symmetry does a non-square rectangle have?1 mark
The two lines join midpoints of opposite sides and pass through the centre. Diagonals are not symmetry lines.
2 - Does a square match itself after a quarter turn about its centre?1 mark
The four equal sides and four right angles align after each quarter turn.
Yes. - Does a non-square rectangle match itself after a half turn about its centre?1 mark
Opposite corners and equal opposite sides exchange places.
Yes. - A shape is symmetric across x = 3. One vertex is at (1, 4). Where is its matching vertex?2 marks
The first vertex is 2 left of the mirror; its partner is 2 right at the same height.
(5, 4) - An isosceles triangle has two equal sloping sides and a different-length base. Describe its one line of symmetry.2 marks
This line exchanges the equal sides and matches the two base corners.
From the vertex where the equal sides meet to the midpoint of the base, perpendicular to the base. - Leah calls the diagonal of a non-square rectangle a mirror line because it cuts the area in half. Explain the mistake.2 marks
Symmetry requires a matching reflected outline, not merely equal areas.
It gives equal-area triangles, but reflection across it does not match the long and short sides.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics 2026
Constructing grids; ordered coordinates; movement; translations/reflections/rotations; symmetry.
Official curriculum source ↗