From a Parallelogram to a Rhombus: Determine whether the parallelogram is a rhombus

The definition of a rhombus is "a quadrilateral with all sides equal"

Therefore, the square in the diagram is indeed a rhombus

Thus, the correct answer is answer A.

The definition of a rhombus is "a parallelogram with all sides equal", and since it is also a type of parallelogram, it is a parallelogram with one pair of adjacent and equal sides (since in a parallelogram opposite sides are equal)

In the parallelogram shown in the drawing, the adjacent sides are clearly not equal in length,

therefore the parallelogram shown in the drawing is not a rhombus.

Therefore the correct answer is answer B.

The parallelogram whose diagonals are perpendicular to each other (meaning the angle between them is $90\degree$) is a rhombus, therefore the given parallelogram is a rhombus.

Therefore, the correct answer is answer A.