Symmetry, Reflections and Turns

In short: A line of symmetry splits a shape into two halves that are mirror images. A shape has rotational symmetry if it looks the same after part of a turn. A reflection flips a shape over a mirror line, and every fold in paper acts like a mirror line.

Before you start

• The names of triangles and quadrilaterals (see Triangles and Quadrilaterals).
• Quarter, half and full turns (see Types of Angles).

Lines of symmetry

If you fold a shape along a line of symmetry, the two halves match exactly.

Rotational symmetry

A shape has rotational symmetry if it fits on itself before a full turn. The order is how many times it fits in one full turn.

• A square fits 4 times: order 4.
• A rectangle and a parallelogram fit twice: order 2.
• The letter Z fits twice, but has no line of symmetry.

Reflections

A reflection flips a shape over a mirror line. Each point of the image is the same distance from the mirror line as the point it came from, on the other side.

Folding and cutting paper

Completing a symmetric pattern

To make a grid pattern with 4 lines of symmetry, it must match across the vertical line, the horizontal line and both diagonals. Reflect each shaded square in every line, and shade all the images.

Quick summary

• A line of symmetry splits a shape into two mirror halves.
• A square has 4 lines, a rectangle 2, a kite 1 and a parallelogram 0.
• A regular shape has as many lines of symmetry as sides.
• Rotational order is how many times a shape fits on itself in a full turn.
• Reflecting in a vertical then a horizontal line is the same as a half turn.
• When paper is folded, each cut is reflected across every fold.

Quiz