Why did Allah ask Adam to teach the Angels their names?

In the Quran: >Allah taught Adam all the names of everything, then He showed them to the angels and said: "Tell Me the names of these if you are truthful." They (angels) said: "Glory be to You, we have no knowledge except what You have taught us. Verily, it is You, the All-Knower, the All-Wise." > >He said: "O Adam! Inform them of their names," and when he had informed them of their names, He said: "Did I not tell you that I know the unseen in the heavens and the earth, and I know what you reveal and what you have been hiding?" The Angels say that they have no knowledge except what Allah has taught them. Are their names unknown to them as Allah has not told them - in which case why does Allah ask Adam to tell the Angels their names rather than Himself, or do they know their names but have hidden it from Allah?