Can You solve this problem sum
The diagonals ACand BD of a quadrilateral ABCD intersects each other at O such that AO/OC=BO/OD. Prove that the quadrilateral ABCDis a trapezium

Given, a quadrilateral ABCD whose diagonals AC and BD intersect each other at O.

To prove: ABCD is a trapezium

Proof : In ∆AOB and ∆COD, we have

∠1 = ∠2 [vertically opposite angles]

∴ ∠3 = ∠4 (corresponding parts of similar triangles]

Now AB and CD are two line and AC being the transversal line making ∠3 = ∠4, it could be possible only in the case when AB || CD, because when a transversal cut the two parallel lines, the alternate opposite angles thus, formed are always equal, which is the case with ∠3 and ∠4.

So ∠3 = ∠4 denotes AB || CD. 

Hence, ABCD is a trapezium.