Building rapport is one step. Maintaining rapport and bridging into the message you wish to tell is another. He has given assurance of this to all by raising Him from the dead. Paul has reached the crux of his message and has held the attention of his audience. It was the rapport that Paul built with the antagonistic philosophers that is the key to his successful communication here.
Rapport is much more than verbal compliments of course.
It is the non-verbal behavior that is involved as well. The ability to politely and effectively close a cycle of communication is a skill that more people need to become adept at. Closure is the final step in any segment or cycle of communication. Someone walked out of a room, hung up the phone, switched subjects in mid-conversation without explaining why, etc. When complete cycles of communication are not accomplished, it leaves the person with tremendous frustration and often anger.