Within the Landauer framework of ballistic transport, we theoretically investigate spin-dependent resonant transmission and magnetoresistance in symmetric cascade junctions of ferromagnetic metal (FM) and semiconductor (SC). It is shown that spin-up and spin-down electrons possess different bandgap structures against the Rashba spin-orbit wave vector. Due to the mirror symmetry, multiple spin-dependent perfect transmissions of electrons can be obtained within the bandgap, thereafter, spin polarization has multiple reversals. Around each resonant wave vector, high spin polarization is achieved and the electrical conductance comes from one kind of spin electrons. The resonant transmissions originate from the spin-dependent quasi-bound states at energies above the potential barriers, which are demonstrated by the electronic charge distributions in the system. Furthermore, if we change the magnetization of FM in the centre of the junctions, inverse magnetoresistance can be observed. The investigations may have potential applications in spin filters and spin switches.