What evidence suggest that continents move

The shifting of tectonic plates under the earth's crust when these plates slide they can cause earthquakes, create, destroy and move countenance is all caused by constant movement of magma ocean underneath the earth surface.

The crust floats on magma. The crust is made up of multiple plates. Some plates have continents on them, so when the plates move, the continents move. That's why contnents move