Question

THE MEDIANS BE & CF of a triangle ABC intersect at G . prove that area of triangle GBC = area of quadrilateral AFGE .figure is must . PLZ help me !!!!!

Answer 1

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      
 ⇒ ΔCGE = ΔFGE ( GBC is common ) ----------------- ( ii )
on subtracting eqn. ( i ) & ( ii ) we get ,
ΔBCE - ΔCGE = ΔBEA - ΔFGE
 ∴ ΔBGC =quadrilateral AFGE . 






 

Answer 2

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