For a question, can I say angles BAO and OCD are equal (angles at the circumference standing on the same arc BD are equal) or is that wrong?

When you refer to the angles on the arc BD being equal are you referring to the angles BAO & OCD? Because those angles aren't on the arc BD. The only angle "on" arc BD is the central angle BOD. Were you given that any angles are equal? **Remember that when you refer to an angle, the middle letter needs to be the vertex of the angle*

I tried to prove the two triangles congruent in order to prove the angles were equal but failed miserably.Even if they were congruent, it wouldn't be based on those two angles being equal because they aren't the same angle on each triangle, if you rotate them around so they are on top of eachother, you will see what I mean.

Can you give me the original question provided? There really isn't enough information here to figure that out.