Free printable symmetry chart

Grades 2–5What a line of symmetry actually is, how many each shape has, and why a parallelogram has none at all. Print it for the wall, or tap the shapes below and watch every fold line appear.

Symmetry math chart for kids Tap the chart to open it at full size

Tap a shape to see its folds

Each shape shows how many lines of symmetry it has, and tapping it draws them in. A line of symmetry is a fold that makes the two halves land exactly on top of each other — not just a line that looks like it splits the shape fairly.

Try the parallelogram. It looks balanced, most children confidently draw a diagonal through it, and it has no lines of symmetry at all. Fold along that diagonal and the halves do not match. What it has instead is rotational symmetry — turn it half a turn and it looks the same, which is a different property with a different name.

Then compare the rectangle with the rhombus. The rectangle folds across its middles but not along its diagonals; the rhombus is the exact reverse. Both have two lines, in opposite places, which is a neat way to see that symmetry follows the sides and angles rather than the general look of a shape.

Tap a shape to fold it

Lines of symmetry
Tap any shape above
Where they run
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A line of symmetry is a fold that makes both halves land exactly on each other.

How to use this symmetry chart at home

Fold real paper. Cut the shape out, fold it, and look. Symmetry is one of the few math topics where the definition is literally a physical action, and a child who has folded a rectangle along its diagonal and seen the corners miss will never again claim it has four lines.

Cut and unfold to make symmetrical shapes. Fold paper in half, cut any wiggly shape through the fold, open it out. Whatever comes out is symmetrical, guaranteed, and the fold is the line. Working backwards like this teaches the idea faster than identifying lines on a worksheet.

Hunt for symmetry in letters. A, H, M, T and Y have a vertical line. B, C, D and E have a horizontal one. H, I, O and X have both. It is a good five-minute game and it uses shapes children already know by heart.

The test is the fold, not the look

Most wrong answers here come from drawing a line that divides a shape into two equal-sized pieces and calling it symmetry. Equal area is not the test. The two halves have to land on each other exactly, in the same orientation.

The rectangle's diagonal is the standard trap. It splits the rectangle into two identical triangles, so it passes the equal-pieces test easily. But fold along it and one triangle sticks out past the other, because they are mirror images that have to be flipped rather than folded to match.

Saying fold it rather than split it, every time, is most of the fix. It converts a vague visual judgment into a physical question with a definite answer.

Regular shapes follow a rule

A regular polygon — one with all sides and all angles equal — has exactly as many lines of symmetry as it has sides. Triangle three, square four, pentagon five, hexagon six, and so on.

For shapes with an odd number of sides, every line runs from a corner to the middle of the opposite side. For an even number, half run corner to corner and half run side to side, which is worth pointing out because the two look quite different on the page.

The circle is the limit of that pattern. Add more and more sides and you get more and more lines, until with a circle every line through the center works and there are infinitely many.

Where symmetry usually goes wrong

Claiming a rectangle has diagonal symmetry. The commonest error in the topic. Folding paper settles it in seconds.

Giving a parallelogram lines it does not have. It looks balanced, but balance comes from rotation here, not reflection.

Missing lines on regular shapes. Finding two on a hexagon and stopping. Counting the sides tells you how many to look for.

Confusing symmetry with equal halves. Any line through the center of a parallelogram makes two equal areas, and none of them are lines of symmetry.

After the chart goes up

A chart explains the idea but gives a child nothing to do. These do the rest.

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Questions parents ask

What is a line of symmetry?

A line you could fold along so that the two halves land exactly on top of each other. It is sometimes called a mirror line, because everything on one side is reflected on the other. The test is the fold, not whether the line looks like it divides the shape fairly.

How many lines of symmetry does a square have?

Four. Two run through the middles of opposite sides, and two run along the diagonals. A regular shape always has as many lines of symmetry as it has sides, so a pentagon has five and a hexagon has six.

Does a rectangle have diagonal symmetry?

No, and this catches almost everyone. A rectangle has exactly two lines of symmetry, both through the middles of its sides. Fold a non-square rectangle along a diagonal and the two halves are the same shape but do not sit on top of each other — try it with a piece of paper.

Why does a parallelogram have no lines of symmetry?

Because no fold matches its halves up. The diagonals look promising but fail the test. It does have rotational symmetry — turning it half a turn leaves it looking the same — which is why it feels balanced even though it has no mirror line.

What is the difference between line and rotational symmetry?

Line symmetry is about folding: one half mirrors the other. Rotational symmetry is about turning: the shape looks the same before it has gone all the way round. A shape can have one without the other, and a parallelogram is the standard example of rotational symmetry with no lines.

What grade is this symmetry chart for?

Grades 2 to 5. Recognizing symmetrical shapes usually starts around Grade 2, drawing lines of symmetry in Grade 3 or 4, and rotational symmetry by Grade 5. It reappears with reflections in the coordinate plane later.

Is this symmetry chart free to print?

Yes. Open it full size and print as many copies as you need for home or a classroom, with no account and no watermark. Reselling it or re-hosting the file elsewhere is not allowed — link to this page instead.