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Question
Prove that the straight lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.
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Solution
Join AC.
P and Q are mid-points of AB and BC respectively.
∴ PQ || AC, PQ = `(1)/(2)"AC"`.........(i)
S and R are mid-points of AD and DC respectively.
∴ SR || AC, SR = `(1)/(2)"AC"`.........(ii)
From (i) and (ii)
PQ = SR
Therefore, PQRS is a parallelogram.
Since, diagonals of a parallelogram bisect each other
Therefore, PQ and QS bisect each other.
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