onals that bisect the angles. A parallelogram through a ideal angle and also diagonals that bisect the angles. A parallelogram v a best angle and opposites sides that room congruent. A parallelogram v all political parties congruent.

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




Consider a parallelogram with a right angle and also diagonals that bisect the angles.

In the figure, ABCD is a parallelogram v ∠ A = 90°.

Since the opposite angle of a parallelogram are equal,

∠ A = ∠ C = 90° and ∠ B = ∠ D

Also, since surrounding angles the a parallelogram are supplementary,

∠ A + ∠ B = 180°

But, because ∠ A = 90°, ∠ B = 90° and also ∠ D = 90°

Therefore, ∠ A = ∠ B = ∠ C = ∠ D.

Now, the is offered that the diagonals bisect the angles.

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

Consider, triangles OBA and also OBC.

∠ OBA = ∠ OBC = 45°

and OB = OB (common)

Therefore, Δ OBA ≅ Δ OBC (SAS Rule)

By equivalent parts that congruent triangles,

AB = BC

Note that in a parallelogram, opposing angles are congruent.

Therefore, abdominal muscle = BC = CD = DA.

Hence, in the parallelogram ABCD, us have,

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

Hence, ABCD is a square.

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Pie5 month ago
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thedesigningfairy.com:

A Parallelogram with a best angle and also diagonals the bisect the angles

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