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Question
The figure formed by joining the mid-points of the adjacent sides of a quadrilateral is a
Options
parallelogram
rectangle
square
rhombus
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Solution
Figure can be drawn as:
Let ABCD be a quadrilateral such that P,Q,R and S are the mid-points of side AB,BC,CD and DA respectively.
In ΔABC,P and Q are the mid-points of AB and BC respectively.
Therefore,
PQ || AC and `PQ = 1/2 AC`
Similarly, we have
RS || ACand `RS = 1/2 AC`
Thus,
PQ || RS and PQ = RS
Therefore, PQRSis a parallelogram.
The figure formed by joining the mid-points of the adjacent sides of a quadrilateral is a
parallelogram.
Hence the correct choice is (a).
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