Lines of symmetry and point symmetry

What it shows

A line of symmetry divides a shape into two halves that match exactly when folded along it, and a centre of symmetry is a point about which a 180° rotation maps the shape onto itself. The simulation tests candidate lines through the centre of the shape and draws only the true axes: a square has 4, a regular hexagon 6, and a rectangle and a rhombus 2 each. All four of these shapes also have a centre of symmetry. A general quadrilateral has one only when it is a parallelogram, and a parallelogram may still have no line of symmetry at all.

How to use

Choose a Shape and set Type of symmetry to show to Line of symmetry, Point symmetry or Both. Press Next Axis to highlight each line in turn and Try Folding to watch one half fold onto the other, then press Rotate 180° to test the centre. Drag a vertex to distort the shape and ask students why the axes and centre disappear. The grid helps them redraw the shapes on squared paper.

Parameters you can change

• Shape Square, Rectangle, Rhombus, Regular hexagon, Any quadrilateral
• Type of symmetry to show Line of symmetry, Point symmetry, Both
• Show grid
• Show vertex labels

Questions to explore

1. Why is a diagonal of a rectangle not a line of symmetry, even though it cuts the rectangle into two equal triangles?
2. Which quadrilateral has a centre of symmetry but no line of symmetry?
3. How must you drag the vertices of any quadrilateral so that it gains a centre of symmetry?