Question

show that diagonals of parallelogram divide it into four Triangles of equal area

Answer 1

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Answer 2

QuEstiOn :-

• show that diagonals of parallelogram divide it into four triangles of equal area.

AnsWeR :-

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=OD

• We 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 get

ar(△AOB)=ar(△BOC)=ar(△COD)=ar(△AOD)

Hence proved.

• Hope you satisfied with thiss answer :)

Thank You❤