Question

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

Answer 1

hope this helps you!!!!!

by yukki

Answer 2

Given : A point D is taken on the side BC of a Δ ABC such that BD = 2DC.  

 

To prove : ar(Δ ABD) = 2ar(Δ ADC)

 

Proof :  

In ∆ABC, we have  

BD = 2DC

Let E be the midpoint of BD . Then ,  

BE = ED = DC

Median of the triangle divides it into two equal triangles.

Since AE and AD are  medians of Δ's ABD and AEC .

∴ ar (ΔABD) = 2 ar (ΔAED) ……..(1)

and,

ar (ΔADC) = ar (ΔAED) ……..(2)

Now,

ar (ΔABD) = 2 ar (ΔAED)

ar (ΔABD) = 2 ar (ΔADC)

[From eq 2]  

Hence, proved

 

HOPE THIS ANSWER WILL HELP YOU…..

 

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