Geometry for Elementary School/Symmetry

In this section, we will talk about symmetry. Symmetry is when a figure has certain properties. There are many kinds of symmetry, but you only need to learn two in elementary school. Note that a figure with any kind of symmetry is called a symmetrical figure.

Reflectional symmetry

The three with axes are shapes with reflectional symmetry. The last one is not.

A figure is considered to have reflectional symmetry when a half of the figure coincides with the other half when folded in half (an easier way to say it would be saying it looks exactly the same on both sides). The line produced by folding is called the axis of symmetry, also known as the line of symmetry. The line must be dotted and must reach outside the figure. Common figures with reflectional symmetry are the English letters A, C, D, E, H, I, K, M, O, and so on. Regular polygons always have reflectional symmetry. The square, for example, has four axes of symmetry. Reflectional symmetry is also known as line symmetry, since it is symmetrical across a line.

Rotational symmetry

The recycling sign has only rotational symmetry.

Rotational symmetry is when a figure returns to its original shape after rotating at a certain angle. The point around which it is rotated is called the centre of rotation, and is marked with an 'x'. The centre of rotation is also the centre of the shape, so you can find the centre of rotation easily. Many figures with reflectional symmetry have also rotational symmetry. Common figures with only rotational symmetry are the recycling sign and fan blades. If a figure coincides with the original twice in one full turn, it has two-fold rotational symmetry, or rotational symmetry order two. Regular polygons always have rotational symmetry. The square, for example, has four-fold rotational symmetry.

Examples

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  A figure with rotational symmetry. What should we add to its centre?
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  We should add a cross.