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

Let there be a rectangle ABCD with AB = CD and BC = AD and A = B = C= D = 90o


Since, BD bisects B


ABD = DBC (i)


And, ADB = DBC [Alternate interior angles]


ABD = ADB. [From (i)]


AB = DA. (Sides opposite to equal angles)


AB = CD = DA = BC


Since, all the sides are equal and all the angles are equal to 90o, thus the quadrilateral is a square.


Hence, ABCD is a square.


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