Answer :

Given:- ABCD is a rectangle i.e AB = CD and AD = BC

To Prove:- ABCD is a square only if its diagonal are perpendicular



Proof:- Let A be at the origin



Now,


By parallelogram law of vector addition,



Since in rectangle opposite sides are equal BC = AD




and



Negative sign as vector is opposite




Diagonals are perpendicular to each other only






AB2 = AD2


AB = AD


Hence all sides are equal if diagonals are perpendicular to each


other


ABCD is a square


Hence proved


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