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The medians B E\ a n d\ C F of a t...

The medians `B E\ a n d\ C F` of a triangle `A B C` intersect at `Gdot` Prove that area of ` G B C=a r e a\ of\ q u a d r i l a t e r a l\ ` AFGE.

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given ,
BE & CF are medians
∴ E and F are midpoints of AC & AB
∴ ΔBCE = ΔBEA ----------- ( i )
ΔBCF = ΔCAF
Const. join E to F we get FE // BC ( By midpoint theoram i.e E joind to F)
∴ ΔFBC = ΔBCE ( Δ on the same base between same // are equal in area )
ΔFBC - ΔGBC = ΔBCE - ΔGBC
...
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