Lines of Symmetry Worksheet Generator

What this generator does

Draws a mixed page of shapes — regular polygons, stars, rectangles, ovals, kites, parallelograms, pinwheels and shapes with nothing at all — each turned to a different angle so the lines are not always upright. For each one it gives the number of lines of symmetry and the number of times the shape turns onto itself in a full turn, because those are two different things and a shape can have the second without the first.

How to use this tool

1. Choose how many shapes go on the sheet.
2. Leave shapes with no line of symmetry in — they are the ones worth arguing about — or tick the box to take them out.
3. Print the sheet and draw every line of symmetry you can find on each shape.
4. Show the answers to mark, and copy the link if a whole class needs the same sheet.

Understanding the controls

Shapes

Three to nine on a page. No two are the same kind while a different kind is still spare.

Only shapes that have at least one line

Off by default, because a shape with no line of symmetry is an answer rather than a trick, and leaving them out makes the sheet easier than the question deserves.

Repeat word

The word this sheet was built from. Anyone opening the same link gets the same shapes in the same positions.

Common use cases

• Practice on lines of symmetry that includes shapes which have none
• Introducing rotational symmetry beside reflection, since a shape can turn onto itself with no mirror line at all
• A printable starter, cover lesson or homework sheet with answers attached
• Settling an argument about the parallelogram, which looks symmetrical and is not
• Giving every child the same sheet from a single link

How this generator works

A shape’s symmetry has to map its corners onto its corners, which fixes the centre of the shape, so every line of symmetry passes through it. A reflection either leaves a corner where it is — so its line runs through that corner — or swaps a pair, so its line runs through the middle of that pair. That makes the lines worth trying a short list, and every one is folded and checked. Where a shape has two lines, doing one reflection after the other is a turn, and that turn is checked in its own right: two lines that hold individually but do not force the turn they should would be an answer about the parts rather than the whole.

Randomness and fairness

Shapes and their angles come from a repeat word taken from your browser’s secure generator unless you type one of your own, so one link gives a class the same sheet. A repeat word makes a sheet reproducible and is not a security measure; nothing here is suitable for anything that needs to stay secret.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

• The shapes are outlines with straight edges between their corners. A curve is drawn as many short straight edges, so an oval here is a many-sided shape that behaves like one.
• Ovals are never circles, because a circle has endlessly many lines of symmetry and the sheet is asking for a number.
• Only reflection and turning are covered. Translation, glide reflection and the symmetry of a repeating pattern are all outside this.
• The shapes are plain geometry rather than pictures. Symmetry in leaves, faces and letters is worth teaching too and is not what this makes.
• The answers sit on the same page, so on a shared screen they have to be hidden rather than absent.

Privacy and your data

The shapes and their answers are worked out in your browser, and nothing about the sheet is sent anywhere or kept. The repeat word is a short label this page minted or you typed, and it is the only part of the sheet that appears in the address.