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Question
ABCD is a quadrilateral P, Q, R and S are the mid-points of AB, BC, CD and AD. Prove that PQRS is a parallelogram.
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Solution
Join AC and BD
In ΔABC,
P and Q are mid-point of AB and BC respectively.
Therefore, PQ || AC and PQ = `(1)/(2)"AC"` ........(i)
In ΔADC,
S and R are mid-point of AD and DC respectively.
Therefore, SR || AC and SR = `(1)/(2)"AC"` ........(ii)
From (i) and (ii)
PQ || SR and PQ = SR
Therefore, PQRS is a parallelogram.
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