What is symmetry?

When you fold a paper heart down the middle, the two halves match exactly. The crease line is the line of symmetry. Any shape that can be folded this way is symmetric.

What is this?

A line of symmetry is a line that divides a shape into two halves that are mirror images of each other. If you fold the shape along this line, the two halves sit exactly on top of each other.

Some shapes have one line of symmetry. The letter A, for example , its mirror line goes straight down the middle.

Some shapes have many lines of symmetry. A square has 4: one down the middle vertical, one across the middle horizontal, and two along the diagonals. A circle has infinite lines of symmetry , every line through its centre is a mirror line.

Some shapes have none. The letter F, the number 5, an irregular blob , no fold makes them match. They are asymmetric.

Symmetry is everywhere in nature. A butterfly's two wings. A flower's petals. Most leaves. The human face (almost!). Why? Because nature loves balance.

Humans have used symmetry in art and architecture for thousands of years. Look at the Taj Mahal, a rangoli, a temple gopuram, a kolam. They all use symmetry to please the eye.

Worked examples

Example 1. Does the letter "H" have line symmetry?

• Vertical line through the middle: yes, both halves match.
• Horizontal line through the middle: also yes.
• 2 lines of symmetry.

Example 2. How many lines of symmetry does an equilateral triangle have?

• Three lines, each from a corner to the middle of the opposite side.
• 3 lines of symmetry.

Example 3. How many lines of symmetry does the letter "S" have?

• Folding vertically , does not match.
• Folding horizontally , does not match.
• 0 lines (S has rotational symmetry but no line symmetry).

Try it

1. How many lines of symmetry does a square have?
2. Does the letter "E" have line symmetry? How many?
3. Does the letter "Z" have any line symmetry?
4. How many lines of symmetry does a rectangle have?
5. Draw any shape with exactly 1 line of symmetry.

Hands-on

Folding test. Cut some shapes from paper , a heart, a kite, a star. Try folding each one to find lines of symmetry. Mark the folds in pencil.

Ink-blot art. Drop a small blob of paint on one half of a folded paper. Press the paper closed and re-open it. You get a perfectly symmetric blob , instant butterfly!