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Technically, a rhombus is a parallelogram, but a parallelogram is not always a rhombus. A parallelogram is any four-sided shape with two sets of parallel lines. A rhombus is a parallelogram with all equivalent side lengths. So, a rhombus is a more specific parallelogram. (And so is a a square or a rectangle.)
A rectangle rhombus is a diamond-like shape, similar to a parallelogram, that has equal angles and line measurements.