Question

ABCD is a trapezium in which AB||DC and diagonals intersect at O.Prove that AO/CO=BO/DO

Answer 1

In that  trapezium we get two triangles AOB and COD which are similar to each other by AAA rule.When triangles are similar, the ratio of their corresponding sides will be same .As angle BAO=angle DCO ,angle AOB=angle COD and angle BOA=angle DOC ,AO,CO form corresponding sides and BO,DO also form corresponding sides.

therefore AO/CO=BO/DO.

I hope ,the explanation helps!!