Symmetry

Look at a butterfly. Its left wing looks exactly like its right wing. If you folded the butterfly in half, the wings would lie on top of each other.

That is symmetry: when a shape, after folding, looks the same on both sides.

The line we fold along is called the line of symmetry.

Shapes with symmetry

The square has 4 lines of symmetry:

• one horizontal (left to right through the middle),
• one vertical (top to bottom through the middle),
• and two diagonal (corner to corner).

The rectangle has 2 lines of symmetry — horizontal and vertical. Not the corner-to-corner ones, because the long side is a different length from the short side.

The circle has infinitely many lines of symmetry — you can fold it anywhere through the centre and it always matches.

The equilateral triangle (all sides equal) has 3 lines of symmetry — from each vertex to the opposite side.

Shapes without symmetry

Some shapes have no line of symmetry:

• F, R, G — these letters are not symmetric.
• A squiggle or an irregular shape — you cannot fold it so the halves match.

A simple test

Take a piece of paper with the shape and fold it along the line you have chosen.

• If the two halves match → it is a line of symmetry.
• If they do not → it is not.

Symmetry around us

• Human face — roughly symmetric (left eye ↔ right eye, left ear ↔ right ear).
• Leaf from a tree — usually symmetric.
• Window panes, a flower, a road sign — symmetry is everywhere.

Summary

• Symmetry = the shape, after folding, looks the same on both sides.
• Line of symmetry = the line we fold along.
• Square: 4 lines. Rectangle: 2. Circle: infinitely many. Equilateral triangle: 3.
• Some shapes have no symmetry.
• Simple test: fold the paper — does it match? Yes → the line of symmetry is there.