Trapezoid abcd has parallel sides ab and cd, of lengths a and b respectively. diagonals ac and bd intersect at
e. draw the line through e that is parallel to ab and cd, and let p and q be its intersections with ad and bc respectively. (a) prove that e is the midpoint of p q. (b) show that p q = 1 1 2 1 a + 1 b . p q is known as the harmonic mean of a and b