Abcd is a parallelogram and e and f are the centroids of triangle abc and bcd respectively then ef is
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Given:
ABCD is a parallelogramE and F are the centroids of triangle ABD and BCD
Since, the diagonals of parallelogram bisect each other
AO is the median of triangle ABDAnd,
CO is the median of triangle CBD
EO= AO (Since, centroid divides the median in the ratio 2:1)
Similarly,
FO = 1/3CO
EO + FO = 1/3 AO +1/3 CO
CO= 1/3(AO + CO)
(AO + CO)EF = 1/3 AC
ACAE = 1/3AO
= 2/3* 1/3AC
= 1/3 AC
ACTherefore,
EF = AE
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