What Is Symmetry?
A shape has line symmetry when a line divides it into two halves that are mirror images of each other. If you fold the shape along that line, the two halves match exactly, with nothing left over. The line is called a line of symmetry or a mirror line. Every point on one side has a partner on the other side, the same distance from the line, directly opposite.
Some shapes have more than one line of symmetry. A rectangle has two, a square has four, and a circle has more than you can count. Some shapes, like the letter F or a scalene triangle, have none at all.
Symmetry All Around Us
Children meet symmetry everywhere once they start looking: a butterfly’s wings, a leaf, a face, the front of a car, a snowflake, the Merlion seen from the front, the windows of an HDB block. Nature uses symmetry because it is efficient and balanced; people use it in buildings, logos and flags because it looks orderly and pleasing. A good game on a walk is to point at something and ask: where is its line of symmetry? Does it have more than one?
Completing a Symmetric Figure
On a square grid, the trick is to count squares from the line. Take one shaded square at a time:
- Count how many squares it is from the line of symmetry.
- Count the same number of squares on the other side of the line, in the same row for a vertical line, or the same column for a horizontal line.
- Shade that square in the same colour.
A square that touches the line has a partner that touches the line on the other side. With a diagonal line, the partner of a square is found by swapping its row and column: the square 2 across and 5 down pairs with the one 5 across and 2 down, and squares on the line stay where they are.
Symmetry in Capital Letters
| Lines of symmetry | Letters (in a plain font) |
|---|---|
| Vertical line only | A M T U V W Y |
| Horizontal line only | B C D E K |
| Both lines | H I O X |
| No line of symmetry | F G J L N P Q R S Z |
Some words are symmetric too: MUM, TOOT and WOW have a vertical line of symmetry, and BOX, CODE and HIDE have a horizontal one when written in capitals. Challenge your child to find more.
How to Use This Page
- Draw in the painter. Start with one mirror line, then try four mirrors and the kaleidoscopes. Turn the mirror lines off to admire the pattern.
- Choose a level and a challenge. Starter uses a vertical line on a small grid; Explorer adds horizontal lines and two colours; Expert adds diagonal lines and asks how many lines of symmetry a pattern has.
- Complete the picture: tap or drag across squares to colour them. Check shows the squares that are wrong or missing.
- Print a worksheet with four pictures to complete on paper, and an answer page.
Tips for Parents and Teachers
- Use a real mirror. Stand a small mirror on the line of a grid picture and look: the reflection shows what the other half should be.
- Fold and blot. Paint blobs on one half of a sheet of paper, fold it, press and open it: a symmetric butterfly every time.
- Check by folding. On printed worksheets, children can fold along the line and hold the paper up to a window to check their answer.
- Count, don’t guess. The most common mistake is to copy the half instead of reflecting it, so the picture faces the same way. Counting from the line fixes this.
Nothing to Install, Nothing Uploaded
The symmetry painter runs entirely in your browser on any phone, tablet or computer, with no account and no download. The last level and challenge you chose are remembered on this device; drawings and answers are never sent to us, and saved pictures go straight to your own device.
Frequently Asked Questions
A line of symmetry divides a shape into two halves that are mirror images of each other. If you fold the shape along the line, the two halves match exactly. A shape can have no lines of symmetry, one, or several: a square has four.
Take one square at a time. Count how many squares it is from the line of symmetry, then shade the square the same distance away on the other side of the line, in the same row (or column, for a horizontal line). Squares touching the line have a partner touching the line on the other side.
In most plain fonts, A, H, I, M, O, T, U, V, W, X and Y have a vertical line of symmetry, and B, C, D, E, H, I, K, O and X have a horizontal one. H, I, O and X have both. F, G, J, L, N, P, Q, R, S and Z have none.
Yes. There is no account, no download and no limit. Drawings and answers stay in your browser and are never uploaded; saved pictures go straight to your own device.