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 PQ.
(b)Show that PQ=1/(0.5)(1/a + 1/b).
