What is reflective symmetry?

Sometimes when we reflect a shape in a particular mirror line it matches itself exactly, in the sense that the mirror image coincides precisely with the original shape. Shape A in Figure H is an example of this phenomenon. The mirror line is shown as a double-headed arrow. This divides the shape into two identical halves that are mirror images of each other. If we cut the shape out we could fold it along the mirror line and the two halves would match exactly.

Another approach is to use the idea employed above. Colour the shape, cut it out and turn it face down: we find that the shape turned face down could still fit exactly into the hole left in the paper. The shape is said to have reflective symmetry (sometimes called line symmetry) and the mirror line is called a line of symmetry.

Shape D in Figure H also has reflective symmetry. There are actually four possible lines that divide this shape into two matching halves with one half the mirror image of the other, although only one of these is shown in the diagram.

Again, notice that if you coloured the shape, cut it out and turned it face down, it could fit exactly into the hole left in the paper.

Teaching Point

Use the colouring, cutting out, turning face down approach to explore the ideas of reflection and reflective symmetry – as well as folding shapes along potential mirror lines, and looking at shapes and their images in mirrors.

Shape C does not have reflective symmetry. The colouring, cutting out and turning face down routine demonstrates this nicely, since it is clear that we would not then be able to fit the shape into the hole left in the paper.