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


By parallelogram law of vector addition,

Since in rectangle opposite sides are equal BC = AD


Negative sign as vector is opposite

Diagonals are perpendicular to each other only

AB2 = AD2


Hence all sides are equal if diagonals are perpendicular to each


ABCD is a square

Hence proved

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