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  • In Fig.9.23, E is any point on median AD of a ∆ ABC. Show that ar (ABE) = ar (ACE).

Q : 1     In Fig. \small 9.23,  E is any point on median AD of a \small \Delta ABC. Show that. \small ar(ABE)=ar(ACE)

              

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We have \DeltaABC such that AD is a median. And we know that median divides the triangle into two triangles of equal areas.
Therefore, ar(\DeltaABD) = ar( \DeltaACD)............(i)

Similarly, In triangle \DeltaBEC,
ar(\DeltaBED) = ar (\DeltaDEC)................(ii)

On subtracting eq(ii) from eq(i), we get
ar(\DeltaABD) - ar(\DeltaBED) = 
\small ar(ABE)=ar(ACE)

Hence proved.

 

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