I travel with my 10 year old nephew all the time (he made GM year before last). We do not look alike, at all. Never a problem. Now, the TSA agent will always address him in a friendly and conversational way and ask him his name and age, since he has no ID, and I think they are looking for subtle clues of anxiety or fear when they do so, but there is never a demand for "proof" that he is my nephew.

But, obviously, if the kid seemed uncertain or afraid to answer, it might prompt more questions, which is fine with me.