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

This is very very simple.

Let the point of Intersection of AC and BD be O.

ΔAOB and ΔDOC are similar, as  (AAA rule).  We see that AB || CD,   AO || OC  and   OB  || OC.

So ratios of corresponding sides are:

OC / OA  =  OD  / OB  =  DC / AB   = 2    given

∴  OC = 2 OA     and  OD = 2 OB.

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