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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) = 2 ar (Δ ADC).



Answer -

Given:
(1) ABC is a triangle
(2) D is a point on BC such that BD = 2DC
To prove: Area of ΔABD = 2 Area of ΔAGC
Proof:
In ΔABC, BD = 2DC
Let E is the midpoint of BD. Then,
BE = ED = DC
Since AE and AD are the medians of ΔABD and ΔAEC respectively
 and
 
The median divides a triangle in to two triangles of equal area. So
 
Hence it is proved that  

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