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Prove that the straight lines joining the mid-points of the opposite sides of a parallelogranare parallel to the other pairs of parallel sides.14. |
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Answer» Let us have a parallelogram ABCD , and E and F are mid points of AB and CD respectively . Here Diagonals AC and BD and EF intersect at " O " . We know diagonals of parallelogram bisect each other , So AO = CO In∆ABC , we have AE = BE , as we assumed E is mid point of ABAndAO = CO , from property of parallelogram .SO,From conserve of mid point theorem , we get EO | | BC , SO EF | | BC ( As EO is part of line EF ) AndWe know BC | | DA , from property of parallelogram , So We can say BC | | DA | | EFSo,Joining the mid points of the opposite sides of a parallelogram are parallel to the other pairs of parallel sides. ( Hence proved ) |
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