Which statement describes a parallelogram that must be a square? (a) a parallelogram with diagonals that bisect each other and opposite sides that are congruent. a parallelogram with perpendicular diagonals. a parallelogram with diagonals that are congruent and perpendicular. a parallelogram with diagonals that are congruent and opposite sides that are congruent.

Consider a parallelogram with diagonals that are congruent and perpendicular.

In triangles Δ AOB and Δ AOD,

OA = OA (common)

OB = OD (Since the diagonals of a parallelogram bisect each other)

∠ AOB = ∠ AOD = 90° (diagonals are perpendicular)

Therefore, Δ AOB ≅ Δ AOD (By SAS postulate)

Since, corresponding parts of congruent triangles are equal,

AB = AD

Similarly, we can prove

BC = CD and CD = DA

So, AB = BC = CD = DA.

Also, it is given that AC = BD.

Hence, ABCD is a square.

Therefore, the correct statement is:

A parallelogram with diagonals that are congruent and perpendicular.

where are the choices?

15 batches are the most you can make

step-by-step explanation: