The diagonals of a quadrilateral ABCD intersect each other at the point o. such that

Draw a line OE parallel to AB

Given: In triangle ABD, OE is parallel to AB

Now, using basic proportionality theorem, we obtain 

It is Given that,

From (i) and (ii), we get

EO || DC (By the converse of basic proportionality theorem)

⇒ AB || OE || DC

⇒ AB || CD

Hence,

ABCD is a trapezium