Quadrilaterals!

Geometry Level 3

Once, while casually discussing Quadrilaterals, a dispute arose between two friends, A and B.
A: Once, I saw a square formed from the midpoints of the sides of another quadrilateral. And the interesting thing is that the outer quadrilateral wasn't a square!!

B: Aha! I caught you! It's impossible to make a square from the midpoints of the sides of another quadrilateral until and unless the outer quadrilateral is a square. I can prove it.

A: I can prove my point too.

B: So, let us go to my home, and see you lose.

They both went to B's home and resolved their confusion. Who must have won the argument?

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