Question

9. Prove that the lines joining the mid points of the opposite sides of a quadrilateral bisect each other.

Answer 1

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or with small answer


Given : ABCD is a quadrilateral
           P,Q,R&S r the midpoints of the respective sides
To prove:PR and QS bisect each other
Proof:
 Join PQ,QR,RS,PS
Join diagonals AC and BD
In ΔABC,
P and Q r the midpoints of AB and BC respectively
Therefore by midpoint theorem, PQ is parallel to AC and PQ=1/2AC
In the same way prove that SR is parallel to AC and SR=1/2AC
Therefore since the opposite sides are equal and parallel PQRS is a parallelogram
In a parallelogram diagonals bisect each other
Hence Proved