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'Stringy Quads' printed from http://nrich.maths.org/
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
Thanks for sending in your solution. Keep
up the good work!