Why is a rhombus a parallelogram?

A parallelogram is a 4-sided figure whose opposite sides are parallel. and opposite angles are the same. The opposite sides of a rhombus are parallel, therefore it's a parallelogram.

Its sides also happen to be all the same length, which isn't required in a parallelogram, and that's why it's a special kind of parallelogram and has a special name. However, a parallelogram is NOT a rhombus!