Symmetry worksheet generator

How it works

1. Choose complete-the-figure (mirror drawings on a grid) or identify-the-line (yes or no about a shape).
2. For mirror drawings, set the grid size and whether the line runs vertically, horizontally or both.
3. Download the PDF, print it, or copy a share link that restores these settings.

Using these worksheets in teaching

Symmetry is one of the few topics where a child can check their own work completely, and it is worth telling them so: fold the paper on the mirror line, hold it to the light, and either the halves land on each other or they do not. That single move turns a marking task into a self-correcting one. Completing a figure on a grid is a counting exercise before it is a geometric one — the reliable method is to take each shaded square, count how far it sits from the line, and count the same distance the other way — and the mistake almost every child makes at first is sliding the pattern across instead of flipping it, which produces a translation and looks convincing until you fold it. Start with a vertical mirror, because a vertical line of symmetry is the one children see everywhere, then move to horizontal, which is markedly harder for no reason anyone can quite explain, then mix them. The identify questions attack a different and stubborn idea: that any line halving a shape is a line of symmetry. A diagonal across a rectangle is the classic — it makes two identical triangles, which feels symmetrical, and folding along it proves at once that it is not.

Frequently asked questions

What does “complete the figure” print?

A squared grid with a pattern shaded on one side of a mirror line and nothing on the other. The child shades the reflection. The answer page reprints the same grids with both halves shaded, so marking is a glance rather than a reconstruction.

Why are the grids always an even number of squares across?

Because the mirror line has to fall between two columns rather than down the middle of one. A line drawn through the centre of a column would ask a child to shade half a square, which no grid can show and no child can mark.

What does “identify the line” ask?

It draws a shape — circle, triangle, square, rectangle, pentagon or hexagon — with a dashed line on it, and asks whether that line is a line of symmetry. Half the lines are deliberately off-centre, because the commonest misconception is that any line cutting a shape in two is a line of symmetry.

Are the answers reliable for shapes like the pentagon?

Yes, and provably so: every answer is computed from the shape’s own vertices rather than from a picture, and the tests reflect those vertices to check it. That is also why no letters appear on this sheet — whether an H is symmetrical depends on the typeface, so it is not a question with one honest answer.

Is there an answer key?

Yes. Turn it on and it is added as clearly labelled pages at the end of the same PDF — completed grids for the mirror drawings, yes or no for each identify question.

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