Final answer:
Quartz is the common mineral found in metamorphic rocks such as slate, schist, and gneiss, remaining stable during the metamorphism process.
Step-by-step explanation:
The mineral commonly found in metamorphic rocks such as slate, schist, and gneiss is quartz. During the process of metamorphism, the shale protolith typically transforms and forms minerals that are stable under altered conditions of pressure and temperature.
Among these new minerals, quartz remains stable and is often a major component. Rocks like slate, which forms from low-grade metamorphism of shale, and gneiss, which is a high-grade metamorphic rock that has undergone intense metamorphism leading to the segregation of minerals into light and dark bands, both contain quartz as a primary mineral. Schist, with its foliated appearance and medium to high-grade metamorphism, also typically includes quartz among its constituents.