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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).

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

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A rhombus is a parallelogram, but a parallelogram isn't always a rhombus. A rhombus is a parallelogram where all the lines are the same length.

A rhombus is a parallelogram, but something that is a parallelogram isn't necessarily a rhombus.

a parallelogram will never ever be a rhombus

A rhombus is always a parallelogram!

No. A rhombus is a type of parallelogram.

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A rhombus is a parallelogram, but a parallelogram isn't always a rhombus. A rhombus is a parallelogram where all the lines are the same length.

A rhombus is a parallelogram, but something that is a parallelogram isn't necessarily a rhombus.

A rhombus is a parallelogram.

a parallelogram will never ever be a rhombus

An equilateral parallelogram is a rhombus.

A rhombus is always a parallelogram!

A rhombus is always a parallelogram, by definition.

No. A rhombus is a type of parallelogram.

A square is a special case of a rhombus. A parallelogram is not a rhombus.

If the sides of a parallelogram are all of the same length then it is a rhombus. Thus, a rhombus is a special type of parallelogram.

Yes, that's a true statement.A rhombus is a special case of a parallelogram.

A rhombus is a special kind of parallelogram: one in which all sides are equal. It is not true to say that a parallelogram is never a rhombus.