The non-volcanic mountains formed at plate boundaries due to plate movement are called fold mountains. These types of mountain form when two plates meet in an head-on collision layers of rocks at their edges crumple and fold in wavelike pattern. The crests of the waves form the peaks of the mountain while the troughs form the valleys. The crumpling or folding of layers of rack can be in the form of a gentle wave or it can be a complex pattern of multiple waves. The famous Himalayan range of mountains has been formed in this way.
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The type of boundary is a convergent. In this case it would be between two pieces of continental crust. If continental crust would collide with ocean crust, subduction occurs. This means because ocean crust is denser, it will be forced under the continental crust and begin to melt, producing magma.