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Show that the diagonals of a parallelogram divide it into four triangles of equal area. |
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Answer» we know that diagonal of a parallelogram bisect each otherthere fore AO is equal to OCandDO is equal to OBin parallelogram ABCD AC is the diagonal and O is the median of triangle divide it into two eqaul parts of equal trianglesthis implies in triangle ABC, oc is median there fore ar(AOC)is equal to ar (BOC) (1) similarly in triangle CBD, OB is median ar(COB) is equal to ar(BOD) (2) in trianle BAD, OD is medianar(BOD) is equal to ar(AOD) (3) NOW from 1,2 and 3 we get ar(AOC)=ar(BOC)=ar(BOD)=ar(AOD)hence, prooved |
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