Question

PQRS is a square. N and M are midpoints of sides SR and QR respectively. O is a point on diagonal PR such that OP=OR. Show that ONRM is a square also find the ratio of ar(ΔORM) and ar(PQRS).

Answer 1

Draw diag according given statement
In ΔSRQ,O and M are mid point of side SQ and QR
by mid point theorm
0M// SR and OM=1/2SR=NR
similarly
IN ΔSQR,by mid point theorm
ON//RQ and ON=1/2RS=RM
apposite sides are equal and parallel hence NOMR is a square


In ΔSOR
ΔSON≡ΔNOR
SN=NR
ON=ON
angle 90 degree in both
similarlyΔSON≡NOR≡ROM≡MOQ
4area of ΔSON=1/2 area of PQRS
area of ΔSON=1/8 area of PQRS
area of ΔORM/area of sqPQRS=1/8

Answer 2

Answer:

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