prove that the figures formed by joining the mid-point of the adjacent side of a quadrilateral is a parallelogram
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HEY THERE !!
THE PROOF OF UR QUESTION IS GIVEN BELOW
Let ABCD a quadrilateral and P,Q,R,S are the mid points of sides AB,BC,CD,DA respectively.
Join AC and be it a diagonal
In triangle ADC , S is the mid point of DC.
Therefore,
SR||AC and SR=1/2 AC ........(1)
( by mid point theorem)
In triangle ABC , P is mid point of AB nad Q is mid point of BC.
Therefore,
PQ||AC and PQ=1/2 AC .......(2)
(by mid point theorem)
FROM EQUATION (1) AND (2),
SR||PQ and SR = PQ.
THEREFORE,
In quadrilateral PQRS, one pair of opposite sides is equal and parallel.
Therefore,
PQRS is a parallelogram.
Hence, proved
THANk YOU
@srk
THE PROOF OF UR QUESTION IS GIVEN BELOW
Let ABCD a quadrilateral and P,Q,R,S are the mid points of sides AB,BC,CD,DA respectively.
Join AC and be it a diagonal
In triangle ADC , S is the mid point of DC.
Therefore,
SR||AC and SR=1/2 AC ........(1)
( by mid point theorem)
In triangle ABC , P is mid point of AB nad Q is mid point of BC.
Therefore,
PQ||AC and PQ=1/2 AC .......(2)
(by mid point theorem)
FROM EQUATION (1) AND (2),
SR||PQ and SR = PQ.
THEREFORE,
In quadrilateral PQRS, one pair of opposite sides is equal and parallel.
Therefore,
PQRS is a parallelogram.
Hence, proved
THANk YOU
@srk
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