English

Lines of Symmetry

Primary schoolMathematicsA line of symmetry folds a shape exactly onto itself: every point lands on another point of the shape

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About this experiment

Fold a paper heart down the middle and the two halves match exactly. The fold is a line of symmetry. In this lab pupils turn a mirror line over fifteen shapes and letters until the reflected outline lands exactly on the shape, then fold it to check. In the painting activity a mirror copies every square they paint, or they finish half-drawn pictures on their own.

Learning goals

  • Recognise a line of symmetry as a fold line where both halves match exactly
  • Find all the lines of symmetry of common 2D shapes and letters
  • Know that some shapes, such as a parallelogram, have no line of symmetry
  • Complete a symmetric picture by reflecting squares across a mirror line
  • Notice that a regular polygon has as many lines of symmetry as sides

How to use it

  1. 1Start with the square. Predict how many lines of symmetry it has, then find them all by turning the mirror line.
  2. 2Try the rectangle. Why is the slanted line from corner to corner not a line of symmetry? Fold it to see.
  3. 3Find the lines of the equilateral, isosceles and scalene triangles. Make a table of your results.
  4. 4Look at the pentagon and hexagon. Can you see a rule for regular shapes?
  5. 5Test the parallelogram and the letter S. They look balanced, so why do they have no lines of symmetry?
  6. 6Switch to painting. Make a picture with the up-and-down mirror, then try both mirrors at once.
  7. 7Choose Finish a picture, switch the mirror helper off and complete the other half yourself. Then check it.

The model

Squares, equilateral triangles, regular pentagons and hexagons
Lines of symmetry of some common shapes

Assumptions

  • Only straight mirror lines are shown. Lines of symmetry of these shapes all pass through the centre of the shape.
  • The mirror line snaps onto a true line of symmetry when it comes within 4 degrees of it, so it is easy to find on a touch screen.
  • The turn symmetry (rotational order) is shown after Show all lines, for older pupils. A shape has order 1 when only a full turn brings it back.
  • In the painting grid, a picture is symmetric when every square has a matching square of the same colour on the other side of the line.

Try this in class

  1. Q1How many lines of symmetry does a circle have?
  2. Q2Write your name in capital letters. Which letters have a line of symmetry?
  3. Q3Draw a shape with exactly two lines of symmetry. Is there one with exactly three?
  4. Q4Why does a kite have one line of symmetry but a parallelogram has none?
  5. Q5Find something in the classroom with a line of symmetry and something without one.

Frequently asked questions

What is the difference between line symmetry and turn symmetry?

Line (reflective) symmetry means a shape can be folded so the halves match. Turn (rotational) symmetry means it looks the same after a part turn. The letter S and a parallelogram have turn symmetry of order 2 but no lines of symmetry.

How can pupils check a line of symmetry without a computer?

Cut the shape out of paper and fold it along the line, or stand a small mirror on the line and see whether the reflection completes the shape exactly.

Where do we see symmetry in nature?

Butterflies, many leaves and human faces are close to having one line of symmetry. Starfish and many flowers have five lines, and snowflakes have six.