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by mid point theorem,
pq||EG and PQ=1/2EG
RS||EG and RS=1/2EG
therefore
PQ||RS and PQ=RS
similarly
PS||QR and PS=QR
therefore PQRS is a ||gm
in MSON(mark the point on line FH that has the contact with S as N)
by the similar manner
MSON is a ||gm(proved)
we know that the diagonals of a rhombus bisect at 90°
and the opp. angles of parallelogram are equal
therefore
MON=90 and also MSN = 90
therefore all the angles of PQRS measure 90°
therefore PQRS is a rectangle
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