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← Back to Geometry
1Curved vs Straight Lines2Lines, Rays & Line Segments32D Shapes43D Shapes5Triangle Classification6Symmetry7Compound Perimeter

Concept 6 of 7

Symmetry: The Mirror Line

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Today's big idea

A fold is a line of symmetry only when both halves land on each other exactly.

Finding one fold is not the end, since many shapes hide several more.

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How it works

👀 What's going on?

Fold a birthday card in half and press it flat. If the two halves cover each other exactly, with nothing poking out at the edge, that fold is special.

💡 Here's the trick

Lines of symmetrySquare4 linesRectangle2 linesCircle∞ linesA line of symmetry folds a shape into matching halvesTriangle (equilateral) = 3 · Pentagon = 5 · Hexagon = 6

Look at the three shapes above. Each dashed line marks a fold. The two halves land exactly on top of each other, and a fold that does that is a line of symmetry. The square takes 4 of these folds. The rectangle takes only 2. The circle takes more than anyone could count, because every fold through its centre works.

🪄 How to do it

  1. 1.Choose one fold line on the shape above, straight down, straight across or corner to corner.
  2. 2.Imagine the fold, then check that every edge lands on an edge and every corner on a corner.
  3. 3.Count it if it matches, then go back and try the fold lines you have not used yet.

✍️ Try it

  1. 1.How many lines of symmetry does the capital letter A have?
  2. 2.A parallelogram has sides of 6 cm and 4 cm and leans over, so not one of its corners is a square corner. How many lines of symmetry does it have?
  1. 1.Fold the A straight down its middle and the two halves match, so it has 1 line of symmetry.
  2. 2.No fold works on a leaning parallelogram, so it has 0 lines of symmetry. Fold it corner to corner and one half sticks out past the other.

⚠️ Watch out

You might be thinking that once you find a fold that works you can stop counting. Stop at the first fold on a square and you report 1 line instead of 4. Work through every fold line before you give a number. Some shapes have none at all, even though they look neat and even, so 0 is a real answer.

🌟 Why this matters

Butterflies, leaves, faces and rangoli patterns are all built around a mirror line, and that is what makes them look balanced. A designer draws half a pattern, then flips it, and the job is done in half the time. Spotting the fold line is how you see the plan behind a design.
Exam tip: Class 3 olympiad questions often ask for the number of lines of symmetry in a letter.

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Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“How many lines of symmetry does the letter T have?”

  1. 1

    Try a vertical fold

    Fold T down the middle (top to bottom). Both halves MATCH ✓. 1 line. 🪞

  2. 2

    Try a horizontal fold

    Fold T across the middle — the top bar and the stem DON'T match. ❌

  3. 3

    Any diagonals?

    Try a diagonal — halves don't match either. ❌

  4. 4

    Total lines ✓

    T has 1 line of symmetry

Now you try one — same steps, different story 👇

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See it in action

⚡ Time to play!

Fold the shape along the dashed line. Do the two halves match?

SYMMETRY · ROUND 1 OF 3

triangle, fold down the middle

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Quick check

✅ VERIFICATION

Meera folds a rectangle 8 cm long and 5 cm wide along its diagonal, corner to opposite corner. Do the two halves match exactly?

⚡ Finish the activity above first to answer.

Keep going!

Up next: Compound Perimeter

Any shape's perimeter = sum of its edges.

Concept 7 of 7 →