A rectangle.
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The best classification for a parallelogram that has perpendicular diagonals is a rhombus. A rhombus has four sides that are congruent. The also diagonals bisect the vertex angles of this type of parallelogram.
If the parallelogram is a square then angle A is congruent to angle B ,is congruent to angle C. AB is congruent to BC is congruent to CD.
A square and rectangle.
A rhombus is a type of parallelogram. Parallelograms are types of quadrilaterals. Everything that applies to quadrilaterals and parallelograms apply to rhombuses.Quadrilaterals have four sides and four angles.Parallelograms have at two pairs of opposite sides and opposite angles congruent. (Note: congruent is pretty much "equal", except for geometric figures). Both pairs of opposite sides are also parallel, hence the name "parallelogram".Rhombuses have all sides congruent.
All four of the angles of a rectangle (and of squares) are right angles.(Its name comes from this : rect-angle.)