Show that the diagonal of a parallelogram divide it into four equal ar

1.	Show that the diagonal of a parallelogram divide it into four equal area
Answer» ABCD is a parallelogram in which diagonals AC and BD intersect at point O.To Prove: ar(AOB) = ar(AOC) = ar(BOC) = ar(AOD)As diagonals of a parallelogram bisect each other so, M and N are the mid-points of sides AD and BC respectively. This means; ar(ABNM) = ar(MNCD) = ½ ar(ABCD)ar(ABO) = ½ ar(ABNM) because triangle on same base and with same height is half in area compared to parallelogram on same base and height.Similarly, ar(DOC) = ½ ar(MNCD)This means; ar(ABO) = ar(DOC) = ¼ ar(ABCD)Similarly, following can be proved:ar(AOD) = ar(BON) = ¼ ar(ABCD)Hence, ar(AOB) = ar(BOC) = ar(DOC) = ar(AOD) = ¼ ar(ABCD)

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