The idea in brief. Fold it and see whether the two halves land on each other. Halving the figure is not enough: a rectangle folded along its diagonal gives two halves of exactly the same size and they still do not fit, so that diagonal is not a line of symmetry. And try all four folds, not two. Plenty of figures fold along a diagonal and along nothing else.
Lesson video, with the working
Lines of symmetry
4 min 03 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
Fold left to right. The arms do not match, so this is not a line of symmetry.
Fold top to bottom. The top and bottom arms match and the middle arm folds onto itself.
Neither diagonal fold makes the two halves fit exactly.
lines of symmetry = 1
Answer: 1
Question 13 of 17 · Intermediate · free to trySome of the squares on the grid below are shaded. How many lines of symmetry…Some of the squares on the grid…
Some of the squares on the grid below are shaded. How many lines of symmetry does the shaded figure have?
Fold left to right. Every shaded square lands on a shaded square.
Fold top to bottom. Every shaded square lands on a shaded square.
Fold along the diagonal from top left to bottom right. Every shaded square lands on a shaded square.
Fold along the other diagonal. Every shaded square lands on a shaded square.
lines of symmetry = 1 + 1 + 1 + 1 = 4
Answer: 4
For parents
How can I help my child recognise lines of symmetry?
A line of symmetry makes the two parts of a figure match exactly when one is folded over the line.
What your child learns here
A line of symmetry makes the two parts of a figure match exactly when one is folded over the line. Primary 4 includes recognising symmetric figures and deciding whether a given straight line is a line of symmetry. Your child learns to test the whole figure, rather than accepting a line because it appears central or divides the area into equal amounts.
Use the fold-and-match idea to decide whether the complete outline and any specified internal pattern agree across a proposed line.
Consider vertical, horizontal and sloping candidate lines when the figure's structure suggests them, rather than testing only the page directions.
Distinguish a line that divides the area equally from one that makes corresponding parts coincide after folding.
Count every valid line of symmetry once, including lines that remain valid when the whole figure is turned on the page.
Does the answer make sense?
For a figure with corners, choose a corner away from the proposed symmetry line and look for its matching corner directly opposite at the same perpendicular distance. If that partner is absent, the fold cannot match the whole figure, so the proposed line is not a line of symmetry.
How to practise these questions
Basic practice recognises symmetric figures and counts the valid fold of a letter-shaped figure. Intermediate questions test several suggested lines or count the symmetry lines of a shaded grid pattern. The Challenge questions compare figures, examine a pattern with a missing cell and judge proposed folds across different shapes. Encourage your child to test a specific pair of corresponding parts for each candidate line before deciding whether the whole fold works. Keep a record of valid lines so that a successful direction is not counted twice. For a nearly symmetric pattern, inspect the missing or altered part closely, then verify that any claimed line still matches every other part of the figure as well. Multiple-choice Basic questions show four shaded figures on a square grid and ask which one has a line of symmetry.
Questions parents ask
Do two equal areas always give a line of symmetry? No. The parts must match position by position when folded across that line. A diagonal of a rectangle that is not a square divides it into equal areas, but does not make the halves coincide by that fold. Your child should test corresponding edges and corners instead of accepting equal area as sufficient evidence.
Can a line of symmetry run diagonally? Yes. Symmetry depends on the relationship between the figure and the line, not on whether the line is upright on the page. For a square, the diagonals are valid symmetry lines as well as the lines through the midpoints of opposite sides. Turning a figure changes the direction in which its lines appear, but not how many it has.
How can I help without giving away the number of lines? Ask your child to test one proposed line at a time and explain a pair of parts that would meet. If the test succeeds for the whole figure, keep that line and look for another candidate. If it fails, identify the unmatched part. This makes the final count a record of checked lines rather than an estimate from the picture.
