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⠀⠀⠀Show that the diagonals of a parallelogram divide it into four triangles of equal area. |
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Answer» at the diagonals of a parallelogram divide it into four TRIANGLES of EQUAL area.ANSWERTo PROVE:- ar(△AOB)=ar(△BOC)=ar(△COD)=ar(△AOD)Proof:-Let ABCD be a parallelogram with diagonals AC and BD intersecting at O. Since the diagonals of a parallelogram bisect each other at the point of intersection.Therefore, AO=OC and BO=ODWe KNOW that the median of a triangle divides it into two equal parts.Now,In △ABC,∵BO is median.ar(△AOB)=ar(△BOC).....(1)In △BCD,∵CO is median.ar(△BOC)=ar(△COD).....(2)In △ACD,∵DO is median.ar(△AOD)=ar(△COD).....(3)From equation (1),(2)&(3), we getar(△AOB)=ar(△BOC)=ar(△COD)=ar(△AOD)Hence proved.. |
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