onals that bisect the angles. A parallelogram with a appropriate angle and also diagonals that bisect the angles. A parallelogram via a best angle and also opposites sides that are congruent. A parallelogram with all sides congruent.

You are watching: Which statement describes a parallelogram that must be a square?




Consider a parallelogram through a ideal angle and also diagonals that bisect the angles.

In the number, ABCD is a parallelogram with ∠ A = 90°.

Since the oppowebsite angles of a parallelogram are equal,

∠ A = ∠ C = 90° and also ∠ B = ∠ D

Also, given that adjacent angles of a parallelogram are supplementary,

∠ A + ∠ B = 180°

But, since ∠ A = 90°, ∠ B = 90° and ∠ D = 90°

Thus, ∠ A = ∠ B = ∠ C = ∠ D.

Now, it is provided that the diagonals bisect the angles.

Thus, ∠ OAB = ∠ OBA = ∠ OBC = ∠ OCB = 45°

Consider, triangles OBA and OBC.

∠ OBA = ∠ OBC = 45°

and also OB = OB (common)

Therefore, Δ OBA ≅ Δ OBC (SAS Rule)

By corresponding components of congruent triangles,

AB = BC

Note that in a parallelogram, the oppowebsite angles are congruent.

Because of this, AB = BC = CD = DA.

Hence, in the parallelogram ABCD, we have actually,

AB = BC = CD = DA and ∠ A = ∠ B = ∠ C = ∠ D = 90°

Hence, ABCD is a square.

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Pie5 months ago
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thedesigningfairy.com:

A Parallelogram through a appropriate angle and diagonals that bisect the angles

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