show that the line segments joining the mid point of the opp sides of a quadrilateral bisect each other.
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Answer:
PR & SQ bisect each other i.e. OP=OR & OQ=OS.
In ΔADC,
∴SR∣∣AC
SR= 1/2 AC...(1)
In ΔABC,
∴PQ∣∣AC
PQ= 1/2 AC...(1)
From eq (1) and (2)
PQ= SR & PQ || SR
So, in PQRS, one pair of opposite sides is parallel and equal.
∴PQRS is parallelogram
PR & SQ are its diagonals and diagonals of parallelogram bisect each other
∴OP=OR & OQ=OS
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