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Question
A point D is taken on the side BC of a ΔABC such that BD = 2DC. Prove that ar(Δ ABD) =
2ar (ΔADC).
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Solution
GIven that ,
In ΔABC, BD = 2 DC
To prove: ar ( ΔABD ) = 2ar (ΔADC)
Construction: Take a point E on BD such that BE = ED
Proof : Since, BE = ED and 2 BD = 2DC
Then, BE = ED = DC
We know that median of Δledivides it into two equal Δles
∴ In , ΔABD , AE is a median
Then, area (ΔABD) 2ar (ΔAED) .....(1)
In , ΔAEC , AD is a median
Then area (ΔAED) = area (ΔADC) ...... (2)
Compare equation (1) and (2)
Area (ΔABD) = 2ar (ΔADC).
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