Cut off three right angled isosceles triangles to produce a
pentagon. With two lines, cut the pentagon into three parts which
can be rearranged into another square.
Take any point P inside an equilateral triangle. Draw PA, PB and
PC from the point P perpendicular to the sides of the triangle
where A, B and C are points on the sides. Prove that the sum of the
lengths PA + PB + PC is a constant.
Suppose there is an election with only 3 parties. Draw a diagram
on which you can mark a point to show the percentage of winning
candidates from each party. (This could be used on the night of the
election, moving the point as the results for the different seats
come in, showing how well each of the parties are doing overall).
Shade the regions where one of the parties has a clear majority and
a region where there is no overall majority.