Mirror Magic: Discovering Symmetry

Look at a butterfly. Its left wing and right wing look exactly the same. If you folded the butterfly down the middle, both halves would match perfectly. Can you think of other things in real life that look the same on both sides? A door? Your own face? This idea of 'both halves matching' is called symmetry, and today you are going to explore it in maths.

A shape is symmetrical when you can fold it so that both halves match exactly — one half sits perfectly on top of the other with no parts sticking out. The fold line is called the line of symmetry. It is like placing a mirror along that line — the reflection you see matches the other half of the shape. Some shapes have one line of symmetry. A rectangle has two lines of symmetry — one going across and one going down the middle. A square has four lines of symmetry! Some shapes, like a scalene triangle (a triangle where all three sides are different lengths), have no lines of symmetry at all. Here is a useful trick: imagine folding the shape along a line. If both halves land exactly on top of each other, that fold line is a line of symmetry. We often draw a line of symmetry as a dashed line (- - -) right through the middle of the shape.