A point D is taken on the side BC of a ΔABC, such that BD = 2DC. Prove that ar(ΔABD) = 2ar(ΔADC).
In ΔABC, BD = 2DC
To prove: ar(ΔABD) = 2ar(ΔADC).
Take a point E on BD such that BE = ED
Proof: Since, BE = ED and BD = 2 DC
Then, BE = ED = DC
We know that median of triangle divides it into two equal triangles.
∴ In ΔABD, AE is the median.
Then, ar(ΔABD) = 2ar(ΔAED) ⋅⋅⋅⋅ (1)
In ΔAEC, AD is the median.
Then, ar(ΔAED) = 2ar(ΔADC) ⋅⋅⋅ (2)
Compare equation 1 and 2
ar(ΔABD) = 2ar(ΔADC).
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