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Robert, Anezka, Billy, Liam and Zoe from Coldean Primary experimented with lots of different quadrilaterals. They found some shapes with one line of symmetry, some with two and some with no symmetry at all. They also found that there are no quadrilaterals with three lines of symmetry, and that only squares have four lines of symmetry. They tested a hypothesis about the relationship between symmetry and pairs of equal edges which didn't quite work out, but it was a very thorough investigation and excellent work all round! You can see their results here .

In answer to how you could prove to someone watching that you have identified all the lines of symmetry, they suggested making the shapes out of paper and folding them in half so that the edges and vertices match up. You could also prove it with a mirror. If you get the person to place a mirror halfway across your shape and gradually rotate it, they will see that the only positions where the reflection allows you to 'see' the whole of the original shape are the lines of symmetry that you have identified.

Thanks for sending in your solution. Keep up the good work!