Primary 4 maths · Geometry · About 10 minutes
Identify lines of symmetry
Compare corresponding points and distances, rather than just the overall outline.
Start the interactive lesson →Open practice activity
What you will learn
- Identify lines of symmetry
Models used: number sentences, stories, diagrams.
Fold it onto its partner
The dotted line is a mirror. This blue point is 3 squares to its left.
The dotted line is the fold. Matching points must be equally far from it.
The dotted line is a mirror. This blue point is 3 squares to its left.
Matching points lie the same perpendicular distance from the mirror, on opposite sides.
Left 3 units · right 1 units
The dotted line is the fold. Matching points must be equally far from it.
The orange point is too close. Move it until both points are equally far from the mirror.
Left 3 units · right 2 units
The dotted line is the fold. Matching points must be equally far from it.
Now both points are 3 squares away. Folding on the mirror line would make them meet.
Left 3 units · right 3 units
What did the picture help us see?
Now both points are 3 squares away. Folding on the mirror line would make them meet.
Worked example: A new example, together
How many lines of symmetry does this square have?
Compare corresponding points and distances, rather than just the overall outline.
A symmetry line matches every point of one half to the other half.
Imagine folds that make both halves coincide exactly. Try folding the figure onto itself.
Imagine folds that make both halves coincide exactly. How many lines of symmetry does this square have?
4
Try folding the figure onto itself.
Imagine folds that make both halves coincide exactly. Count only distinct fold lines with exact matching halves.
Imagine folds that make both halves coincide exactly. There are 4 lines of symmetry.
Imagine folds that make both halves coincide exactly. Check the result against the question we started with.
Two midlines and two diagonals give four lines.
We found 4. A symmetry line matches every point of one half to the other half.
Imagine folds that make both halves coincide exactly.
Common mistakes to discuss
- Any diagonal is a line of symmetry. Folding must match the halves exactly. A rectangle’s diagonal does not, so a rectangle has two lines of symmetry, not four.
Check your understanding
- Identify lines of symmetry
- justify symmetry by matching points across a mirror
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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