Stringy Quads

You will need a loop of string for this activity and three friends to work with.


With all four of you holding part of the string, make a quadrilateral which has one line of symmetry.
How could you convince someone else watching that your shape has just one line of symmetry?
Can you make any other quadrilaterals with just one line of symmetry?

Now use the string to form a quadrilateral with two lines of symmetry.
Again, how could you prove where these two lines lie?
Can you make any other quadrilaterals with two lines of symmetry?

Now use the string to form a quadrilateral with three lines of symmetry.
Is it possible? Explain.

Now use the string to form a quadrilateral with four lines of symmetry.
Where do the four lines lie?

Many thanks to Lynne McClure who devised this problem and gave us permission to publish it here.