Lines and Order of Symmetry: Full Table of Plane Shapes

A line of symmetry is a fold along which a shape's two halves cover each other exactly. Rotational order is how many times a shape looks identical during one full 360° turn. Both are taught in Years 4–5 as part of plane shapes.

The Full Table

🔴 The two rows asked most often in tests and answered wrongly most often: a parallelogram has 0 lines of symmetry but rotational order 2, and a scalene triangle has 0 lines of symmetry but still rotational order 1.

The Rule That Simplifies Everything

For regular shapes (all sides and angles equal) a simple pattern holds:

Lines of symmetry = rotational order = number of sides

Equilateral triangle 3, square 4, regular pentagon 5, regular hexagon 6. Nothing to memorise — just count the sides.

For irregular shapes the table above is still needed, but there are far fewer to learn.

Why Rotational Order Is at Least 1

The question that always comes up: why does a scalene triangle have order 1 rather than 0?

Because a full 360° turn returns the shape to its starting position — and that position counts. Every plane shape has a rotational order of at least 1. Zero never occurs for rotational order, while zero is perfectly possible for lines of symmetry.

How to Check at Home

Lines of symmetry: cut the shape from paper and fold it. If the halves cover exactly with nothing sticking out, that is one line. Try every fold direction.

Rotational order: draw the shape, trace it onto a second sheet, then rotate the second sheet over the first while holding the centre. Count how many times the outline matches perfectly before returning to the start.

Five minutes with scissors beats an hour memorising the table, and the result does not evaporate after the test.

The Mistakes That Actually Cost Marks

1. Thinking rotational order can be 0. It is always at least 1. The number one cause.

2. Thinking a parallelogram has 2 lines of symmetry. Its diagonals look like axes, but folding along them does not make the halves match. The answer is 0.

3. Assuming lines of symmetry always equal rotational order. True only for regular shapes. The parallelogram disproves it.

4. Forgetting the circle is infinite on both counts.

5. Confusing lines of symmetry with axes of symmetry. They are the same thing; the axis is the fold line, and the number of axes equals the number of lines of symmetry.