Some shapes, such as a scalene triangle, have no lines of symmetry – it is not possible to fold the shape about a line so that the two halves fit exactly on top of one another.

The Dinosaur by Augusto Monterroso Google The Dinosaur and you’ll be informed that no less an authority than novelist and literary critic Umberto Eco crowned it the world’s shortest novel.

The same is true of the letter M. Letters like B and D have a horizontal line of symmetry: their top and bottom parts match. Some letters, for example, X, H, and O, have both vertical and horizontal lines of symmetry. And some, like P, R, and N, have no lines of symmetry.

A rectangle has two lines of symmetry.

So the square has four lines of symmetry. The rectangle has only two, as it can be folded in half horizontally or vertically: students should be encouraged to try to fold the rectangle in half diagonally to see why this does not work. The trapezoid has only a vertical line of symmetry.

No triangle has 2 lines of symmetry. Equilateral triangle has three lines of symmetry while an isosceles has one. A scalene triangle has none.

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The division of triangles into scalene, isosceles, and equilateral can be thought of in terms of lines of symmetry. A scalene triangle is a triangle with no lines of symmetry while an isosceles triangle has at least one line of symmetry and an equilateral triangle has three lines of symmetry.

A line of symmetry is a line that cuts a shape exactly in half. This means that if you were to fold the shape along the line, both halves would match exactly. Equally, if you were to place a mirror along the line, the shape would remain unchanged.