No. A rhombus is a type of parallelogram.
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Yes. A square is a special type of rhombus which is itself a special kind of parallelogram.
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, square, kite or arrowhead.