A rectangular sheet of paper measuring 20 cm×12 cm is divided by drawing both diagonals, producing four triangular pieces.
(i) List all pairs of triangles that are congruent.
(ii) One of the triangular pieces is rotated through 180∘ about the centre of the rectangle. Will it exactly cover another triangular piece? Give a reason for your answer.
(iii) If each triangle is to be coloured and every pair of congruent triangles must be coloured with the same colour, what is the minimum number of different colours required? Justify your answer.