All sides of a rhombus are the same length. Of the other parallelograms, only the square has identical side lengths (it differs from a rhombus by having four right angles).
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It is a rhombus.
No. All rhombi (rhombuses) are parallelograms but all parallelograms are not rhombi.
No but they are parallelograms.
Yes. All rhombuses are parallelograms, but the reverse is not true. (I.e. there are parallelograms which are rhombuses and there a parallelograms that are not rhombuses. -- Just like Every bus has wheels but not everything with wheels is a bus.)
No, it's not true. A rhombus is a special kind of parallelogram, so only some parallelograms are rhombera.