  We put forward complementary relations of entanglement, coherence, steering
inequality violation, and Bell nonlocality for arbitrary three-qubit states. We
show that two families of genuinely entangled three-qubit pure states with
single parameter exist, and they exhibit maximum coherence and steering
inequality violation for a fixed amount of negativity, respectively. It is
found that the negativity is exactly equal to the geometric mean of bipartite
concurrences for the three-qubit pure states, although the negativity is always
less than or equal to the latter for three-qubit mixed states. Moreover, the
complementary relation between negativity and first-order coherence for
tripartite entanglement states are established. Furthermore, we investigate the
close relation between the negativity and the maximum steering inequality
violation. In addition, the complementary relation between negativity and the
maximum Bell-inequality violation for arbitrary three-qubit states is obtained.
The results provide reliable evidence of fundamental connections among
entanglement, coherence, steering inequality violation, and Bell nonlocality.
