# A point D is taken on the side BC of a Δ ABC such that BD = 2DC. Prove thatar(Δ ABD) = 2ar(Δ ADC)

Given that,

In Δ ABC,

We have

BD = 2DC

To prove: Area () = 2 Area ()

Construction: Take a point E on BD such that, BE = ED

Proof: Since,

BE = ED and,

BD = 2DC

Then,

BE = ED = DC

Median of the triangle divides it into two equal triangles

Since,

AE and AD are the medians of ΔABD and AEC respectively

Therefore,

Area (ΔABD) = 2 Area (ΔAED) (i)

And,

Area (ΔADC) = Area (ΔAED) (ii)

Comparing (i) and (ii), we get

Area (ΔABD) = 2 Area (ΔADC)

Hence, proved

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