Question

In a parallelogram ABCD if two diagonals are equal. Find the measure of angle ABC.

answer fast please

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Answer 1

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Since ABCD is a parallelogram .

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★ Therefore AB = CD And AD = BC

Thus in ∆ ABD and ∆ ACB ,

★ AD = BC

★ BD = AC

★ AB = AB

So by SSS criteria of Congruence ,

∆ABD ≈ ACB

Therefore , Angle BAD = Angle ABC

Now AD || BC and Transversal AB intersects them at AB respectively .

Therefore ,

Angle BAD + Angle ABC = 180°

Angle ABC + Angle ABC = 180°

2 ( ABC ) = 180°

Angle ABC = 90°

★ Answer = 90°