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A parallelogram requires that opposite sides are parallel and of the same length; it is not a requirement that all four sides are of the same length.

A rhombus requires that opposite sides are parallel and all four sides are of the same length.

It is possible that a parallelogram can have all four sides of the same length; when it does it now fulfils the requirements of a rhombus, and so is a rhombus.

Thus a rhombus is a type of parallelogram (all rhombuses are parallelograms), but there are parallelograms which are not rhombuses (those where there are two sides of one length (opposite and parallel) and the other two sides of a different length).

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Q: How can you convince me that a rhombus is a parallelogram but a parallelogram is not a rhombus?
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