ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that 

The figure is given below:

Construct a line EF through point O, such that EF is parallel to CD.

In ΔADC, EO is parallel to CD

Now, using basic proportionality theorem, we obtain

AE/ED = AO/OC (i)

In ΔABD, OE is parallel to AB

So, using basic proportionality theorem, we get

ED/AE = OD/BO

AE/ED = BO/OD (ii)

From (i) and (ii), we get

Therefore,