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

Question

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

Philoid · Accepted Answer

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

Now, join AC.

In ΔBAD and ΔBCD,

∠ABD = ∠CBD

∠A = ∠C = 90

And BD = BD (common)

BADBCD

AB = BC

And AD = CD

But in rectangle opposite sides are equal,

AB = CD

And BC = AD

AB = BC = CD = DA

So, ABCD is a square.

Hence, Proved.