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3. Symmetry in two-dimensional objects

For many regular objects, you can draw one or more lines across them that divide them exactly in half in such a way that the two parts are mirror images of each other. This property is termed symmetry, and the line is described as an axis of symmetry. If a flat mirror is held along the axis of symmetry and vertical to the plane of the object, the half of the object that is visible and its reflection in the mirror are together identical in appearance to the original object. Examples of axes of symmetry are shown in Figure 1:

Symmetry across two dimensions
Figure 1. Symmetry in two dimensions. a: illustration of the principle of symmetry – a plane mirror is aligned vertically along the diagonal of a square, so that the visible half of the square and its reflection make a complete square; b: the two diagonal axes of symmetry for a square; c: two axes of symmetry that bisect opposite sides in a square; d: the two axes of symmetry in a rectangle, that bisect opposite sides; e: single axis of symmetry for an isosceles triangle (two equal sides) that bisects the base; f: any line passing through the centre of a circle is an axis of symmetry; g: an ellipsoid has two axes of symmetry, along the 'major' and 'minor' axes.