We know that: $$\angle ABO = \angle OBC$$ $$\angle DCO = \angle OCB$$ Prove: $$AB\parallel CD$$
I have tried so many things: First I continued lines $BO$ and $CO$ to reach $CD$ and $AB$. Then I tried adding a parallel line to $AB$ that goes through point $O$. Also I tried adding a median to $BC$ that goes through point $O$, and in another attempt I tried it with an angle bisector. Also I have tried continuing lines $AB$ and $CD$ the other way and adding parallel lines to $BO$ and $OC$ which goes through points $C$ and $B$.
First I thought it seems so natural as just part of a Rhombus, but I found out that it isn't that easy as I thought it would be.
Please help me