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Question
The figure formed by joining the mid-points of the adjacent sides of a parallelogram is a
Options
rectangle
parallelogram
rhombus
square
Solution
It is given a parallelogram ABCD in which P,Q,R and S are the mid-points AB, BC, CDand DA respectively.
PQ, QR, RS and SP are joined.
In ΔABC, P and Q are the mid-points AB and BC respectively.
Therefore,
PQ || AC and `PQ = 1/2 AC `……(i)
Similarly, In ΔADC, R and S are the mid-points CD and AD respectively.
Therefore,
SR || AC and `PQ = 1/2 AC ` ……(ii)
From (i) and (ii), we get
PQ || SR and PQ = SR
Therefore, PQRS is a parallelogram.
Hence the correct choice is (b).
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