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ABCD is a rectangle in which diagonal BD bisects ∠B. Show that ABCD is a square.

1 Answer

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Best answer

Given, in a rectangle ABCD, diagonal BDl bisects ∠B.

Now, join AC.

In ΔBAD and ΔBCD,

∠ABD = ∠CBD

∠A = ∠C = 90image

And BD = BD (common)

ΔBAD ≅ ΔBCD

imageAB = BC

And AD = CD

But in rectangle opposite sides are equal,

AB = CD

And BC = AD

imageAB = BC = CD = DA

So, ABCD is a square.

Hence, Proved.

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