The question, as presented, is incomplete. The entire question is as follows:
Which set of statements would describe a parallelogram that can always be classified as a rhombus?
I. Diagonals are perpendicular bisectors of each other.
II. Diagonals bisect the angles from which they are drawn.
III. Diagonals form four congruent isosceles right triangles.
(1) I and II
(2) I and III
(3) II and III
(4) I, II, and III
The correct answer is (4) I, II, and III.
A rhombus is a quadrilateral with four sides of equal length. A parallelogram is a quadrilateral with two pairs of parallel sides and the opposite sides have equal length.
A parallelogram can be considered a rhombus if it has a diagonal that bisects an interior angle, if it has two consecutive sides of equal length and if the diagonals are perpendicular to each other. Therefore, statements I, II and III can all apply to a parallelogram that will qualify as a rhombus.
