Magnetohydrodynamic (MHD) equations are solved by using the CTU+CT (corner transport upwind + constrained transport) algorithm which guarantees the divergence-free constraint on the magnetic field. The interactions between shock wave and heavy or light triangular cylinder are investigated in detail in the cases with and without magnetic field. In the cases of hydrodynamic (B=0 T) and MHD (B=0.01 T), the numerical results indicate that heavy and light triangular cylinders have quite different wave patterns and jet structures after being impacted by a planar incident shock wave. Specifically, a regular refraction and downstream R22 jet are formed in the heavy case, whereas an irregular refraction and upstream air jet are generated in the light case. In the hydrodynamic case, the Richtmyer-Meshkov (R-M) instability and Kelvin-Helmholtz (K-H) instability are induced by the incident shock wave. Hereafter, both heavy and light density interfaces begin to roll up with a series of interfacial vortex sequences. In addition, a main vortex ring is formed in the heavy case, while a vortex dipole passing through the downstream interface is generated in the light case. In the MHD case, both heavy and light density interfaces remain smooth and interfacial vortex sequences vanish. Furthermore, the main vortex ring formed in the heavy cases and the vortex dipole generated in the light cases disappear. Moreover, in the presence of a magnetic field, a detailed investigation demonstrates that Lorentz forces give rise to the transport of baroclinic vorticities to the Alfvn waves. As a consequence, the deposition of interfacial vorticities decreases and the rolling-up of interfaces is suppressed. In the end, the vorticities are transformed into two vortex sheets travelling away from the density interfaces, and the R-M instability and K-H instability are well controlled. The quantitative investigations reveal that for both heavy and light triangular cylinders, magnetic field can accelerate the upstream interface and decelerate the downstream interface, especially for the light triangular cylinder.