For an algebra A belonging to a quasivariety K, the quotient A/ need not belong to K for every Con A. The natural question arises for which Con A,A/K. We consider algebras A=(A,,1) of type (2, 0) where a partial order relation is determined by the operations and 1. Within these, we characterize congruences on A for which A/ belongs to the same quasivariety as A. In several particular cases, these congruences are determined by the property that every class is a convex subset of A.