Question

show that the line segment joining the midpoints of the opposite sides of a quadrilateral bisect each other

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Answer 1

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

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