Symmetry

A shape is symmetrical if it folds onto itself along a line, or looks the same after a turn of less than a full turn.

Key ideas

• A line of symmetry divides a shape into two halves that are mirror images.
• A point and its mirror image are the same distance from the mirror line, on opposite sides.
• A shape has rotational symmetry if it looks the same after turning by less than a full turn.
• The order of rotational symmetry is how many times it looks the same in one full turn.
• A regular polygon with n sides has n lines of symmetry and rotational symmetry of order n.
• Letters: A has one line of symmetry, H has two, and O has infinitely many.

Remember

Watch out

• Taking a diagonal of a rectangle as a line of symmetry (it is not).
• Counting the full 360° turn as an extra order.
• Measuring only to the mirror line when asked for the distance to the image.

Worked example