Diagonals of a trapezium divide each other proportionally:
Given : In trapezium ABCD , AB// DCR.T.P :AO/OC = BO/OD
Construction: Draw the line PQ; parallel to AB or CD through OProof : In ΔACD, OP// CD
AP/PD = AO/OC................... (1)
(Basic proportionality theorem)
In ΔABD, OP// AB
AP/PD = BO/OD.................(2)
From (1) and (2) we have
AO/OC = BO/OD
i.e, The diagonals AC, BD divide each other proportionally.