1.

show that the diagonal of a parallelogram divide it into four triangle of equal area​ (any one who helped me)​

Answer»

Step-by-step explanation:

To 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.


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