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A Point D is Taken on the Side Bc of a δAbc Such that Bd = 2dc. Prove that Ar(δ Abd) = 2ar (δAdc). - Mathematics

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).

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Exercise 14.3 | Q 11 | Page 45
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