Symmetry

• A line of symmetry divides a shape into two mirror-image halves.
• The order of rotational symmetry is the number of times a shape looks the same in one full turn.
• Know the symmetries of triangles, special quadrilaterals and regular polygons, and the properties they give.
• A regular polygon with n sides has n lines of symmetry and rotational symmetry of order n.
• Solids have planes of symmetry and axes of rotational symmetry: know them for prisms, cylinders, pyramids and cones.

Fold and turn

A shape has line symmetry if a mirror line splits it into two halves that are reflections of each other. Its order of rotational symmetry is how many times it fits onto itself in one full turn of 360°. Every shape fits at least once, so a shape with no rotational symmetry has order 1.

Symmetry explains the properties

The properties come straight from the symmetry. The line of symmetry of an isosceles triangle shows its base angles are equal. The line of symmetry of a kite shows that one pair of opposite angles is equal and that the diagonals cross at 90°.

n lines, order n

A regular polygon with n sides has n lines of symmetry and rotational symmetry of order n. If n is odd, each line goes from a vertex to the midpoint of the opposite side. If n is even, half the lines join opposite vertices and half join midpoints of opposite sides.

Planes and axes

A plane of symmetry cuts a solid into two halves that are mirror images. An axis of symmetry is a line about which the solid can be turned and still look the same; it has an order, like rotational symmetry in 2D.