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A two-dimensional lattice-gas model with triangular symmetry is investigated by using the real-space renormalization group ͑RSRG͒ approach with blocks of different size and symmetries. It has been shown that the precision of this method depends strongly not only on the number of sites in the block but also on its symmetry. In general, the accuracy of the method increases with the number of sites in the block. Using the RSRG method, we have explored phase diagrams of a two-dimensional Ising spin model and of a triangular lattice gas with pair lateral repulsive interactions. We have calculated: ͑i͒ adsorption isotherms and thermodynamic factors for different temperatures and ͑ii͒ the coverage dependence for the pair, three, and four nearest-neighboring particles correlation functions, the tracer, jump, and chemical diffusion coefficients using four different models of adparticle jumps. All these quantities have also been obtained by Monte Carlo ͑MC͒ simulations. Despite the fact that both methods, RSRG and MC, constitute very different approaches, the correspondence of the numerical data is surprisingly good. Therefore we conclude that the RSRG method can be applied, at least for the systems discussed here, to characterize the thermodynamic and kinetic properties of strongly interacting adsorbates. It is also shown that drastic changes in the surface diffusion coefficients occur when ͑i͒ lateral interactions force ordering of the adatoms via second-order phase transition and ͑ii͒ different models of adparticle jumps are used.