Bruck constructed the rst prolongation and contraction of quasigroups in order to study Steiner triple systems. In this paper we dene a new family of quasigroups: The SteinerBruck quasigroups (SB-quasigroups), where aa² = a²a and a² = b² for all possible a and b, which arise from Bruck's prolongation. We use Bruck's prolongation and contraction maps to explore properties of this family of quasigroups. Among other results, we show that there is a one-to-one correspondence between SB-quasigroups and uniquely 2-divisible quasigroups. As a corollary to this result we nd a correspondence between idempotent quasigroups and loops of exponent 2. We then use this correspondence to study some interesting loops of exponent two and some interesting idempotent quasigroups.