We know that in a parallelogram, opposite sides are equal and the diagonals bisect each other.
suppose ABCD is the parallelogram named in order, then consider the triangles COD and AOD
CO=OA [diagonals bisect each other]
∠COD=∠AOD= 90°. [given]
∴Triangle COD congruent to Triangle AOD.
⇒ AD=CD [CPCT]
∴All sides are equal.
∴ABCD is a SQUARE.
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