Relationship between the Borsuk-Ulam theorem, Brouwer's fixed point theorem (for the ball) and Tucker's lemma

Which of these - the Borsuk-Ulam theorem, the Brouwer's fixed point theorem (for the ball) and Tucker's lemma implies which? I'm a little confused with this. I suspect they may be equivalent. If that is indeed so, can someone please provide a proof (or a link to a proof) of the equivalence of the three?