They are just different names for the same shape.
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Actually, they are not. A rhombus is a parallelogram with all its sides of the same length. It is, therefore a special kind of parallelogram. (Just like a square is a special kind of rectangle). So all properties of a parallelogram apply to 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, by definition.
A rhombus is always a parallelogram!