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We consider nonnegative solutions to - Δ ⁢ u = f ⁢ ( u ) in half-planes and strips, under zero Dirichlet boundary condition. Exploiting a rotating and sliding line technique, we prove symmetry and monotonicity properties of the solutions, under very general assumptions on the nonlinearity f . In fact, we provide a unified approach that works in all cases: f ⁢ ( 0 ) < 0 , f ⁢ ( 0 ) = 0 or f ⁢ ( 0 ) > 0 .Furthermore, we make the effort to deal with nonlinearities f that may be not locally-Lipschitz continuous.We also provide explicit examples showing the sharpness of our assumptions on the nonlinear function f ., (© 2017 by De Gruyter.)