[en] We propose a phenomenological model, comprising a microscopic SO(5) model plus the on-site Hubbard interaction U (projected SO(5) model) to understand the interrelation between the d-wave-gap modulation observed by recent angle-resolved photoemission experiments in the insulating antiferromagnet Ca₂CuO₂Cl₂ and the d-wave gap of high-T_c superconducting materials. The on-site interaction U is important in order to produce a Mott gap of the correct order of magnitude, which would be absent in an exact SO(5) theory. The projected SO(5)-model explains the gap characteristics, namely both the symmetry and the different order of magnitude of the gap modulations between the AF and the SCc phases. Furthermore, it is shown that the projected SO(5) theory can provide an explanation for a recent observation [E. Pavarini et al., Phys. Rev. Lett. 87, 47003 (2001)], i. e. that the maximum T_c observed in a large variety of high-T_c cuprates scales with the next-nearest-neighbor hopping matrix element t'. (Abstract Copyright [2003], Wiley Periodicals, Inc.)