ABCD is a trapezium in which AB||DC and its diagonals intersect each other at the point O. Show that AO/BO = CO/DO.

Given: ABCD is a trapezium and AB || DC
To Prove: AO/BO = CO/DO
Construction: Draw OE || DC such that E lies on BC.
Proof: In △BDC,
By Basic Proportionality Theorem, BO/OD = BE/EC (1)
Now, In △ABC,
By Basic Proportionality Theorem, AO/OC = BE/EC (2)
∴From (1), and (2), AO/OC = BO/OD
i.e., AO/BO = CO/DO