Question

In a trapezium abcd ab parallel to dc. if dc = 2ab show that the point of intersection of the two diagonals is a point of trisection

Answer 1

Let the point of intersection of the two diagonals AC and BD be O.

The ΔAOB and ΔDOC are similar.  The corresponding sides AO || CO, BO || DO and  AB || CD.

CD / AB = 2 = CO / OA =  DO / OB 

So OC = 2 OA  and    OD = 2 OB

So O is the point of trisection of the diagonals AC and BD.