Yes
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No, since there is no such thing. It IS a parallelogram, though.
A rhombus is perpendicular * * * * * No, it is not. A rhombus is a four sided plane figure which has two pairs of parallel sides. It is, therefore, a parallelogram. The only thing that is perpendicular in a rhombus is that its diagonals bisect one another at right angles.
All four sides of a rhombus have the same length. If all four sides of a rectangle have the same length, then it's also a rhombus. The thing is, you probably wouldn't look at that thing and call it a rectangle, because it's also a square.
Unusual because there's no such thing.
A rhombus may be a square or just a rhombus (a rhombus is merely called a rhombus when there are no 90 degree angles).