KS4. Geometry. Angles & Symmetry. Line & Rotational Symmetry

We can analyse shapes based on their symmetries. Two types of symmetry are particularly interesting to us. These are:

  • Rotational symmetry; and
  • Line symmetry

The order of rotational symmetry of a shape tells us how many times a shape looks the same when it is rotated in a full circle. As always in mathematics, it is easier to see things in practice than read about them in theory, so let’s consider what is the order of rotational symmetry of each of the following shapes:

A shape can also be classified based on how many lines of symmetry it has. Let’s classify the above shapes this way.

We also need to be able to reflect a shape in a given line. To do this, we make sure that every point in the shape is replaced by a point at the same distance on the other side of the line. As is often the case, this is a practical skill that we improve only by doing it many times. We will get a chance to try this during the following exercise.


Let’s complete exercises 11 and 12 from our textbook, which are detailed below:

The answers are below:

For your reference, below are listed the symmetries of the different quadrilaterals (4-sided shapes):

Solutions to extension problems on the cover webpage of “angles & symmetry”

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