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Question
In a parallelogram PQRS, M and N are the midpoints of the opposite sides PQ and RS respectively. Prove that
PMRN is a parallelogram.
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Solution
Since M and N are the mid-points of PQ and RS respectively.
∴ PM = `(1)/(2)"PQ" and "RN" = (1)/(2)"RS"` ....(i)
But PQRS is a parallelogram,
∴ PQ = RS and PQ || RS
⇒ `(1)/(2)"PQ" = (1)/(2)"RS" and "PQ || RS"`
⇒ PM = RN and PM || RN
⇒ PMRN is a parallelogram.
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