The interacting Su-Schrieffer-Heeger model with nearest neighbor interaction in one dimension at half-filling is studied. To obtain ground state wave function, the Baeriswyl variational wave function is extended to account for alternating hopping parameters. The ground state energy is numerically calculated and compared with exact diagonalization calculations, finding excellent agreement. Full phase diagram of the model is constructed which shows three different phases. When all hopping parameters are same the ideal metal-insulator phase transition is found at finite interaction, somewhat less than the exact results. The conducting phase is a Fermi sea. The phase transitions found are first order. With alternating hopping parameters the small interaction phase is the ground state of the Su- Schrieffer-Heeger model and the large interactions phase is an insulator. The phase transition has been visualized by constructing the parent Hamiltonian of the ground state wave function and tracing out the curves of the Brillouin zone. The polarization distribution is reconstructed from its cumulants on two different paths taken in the parametric space of interaction and hopping parameter. The first path is taken as it crosses the metallic phase line while the other path makes a semi-ellipse avoiding the metallic line. In the former case, the distribution is centered at one site and discontinuously jumps to the next site after crossing the metallic phase line, while in latter case distribution walks smoothly from one site to the next. These results suggest that interaction breaks the chiral symmetry of the Su-Schrieffer-Heeger model, in the same way as on-site potential breaks it in Rice-Mele model.