trapezium property

construct any trapezium (a trapezoid in the US) and draw the two diagonals

at the point where the diagonals meet, construct a line parallel to the two parallel sides of the trapezium

what do you notice?
can you prove it?




this is an old problem, utilised in Michael de Villiers' admirable work on proof and geometry

use similar triangles to show that the length is the harmonic mean of 'a' and 'b'