Q15 of 56 Page 82

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


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.


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