Question

17. The medians of a triangle ABC meet at G. Prove that
area (triangle AGB) = 1/3 ar ( triangleABC)
​

Answer 1

choice to do from 2 pictures

Answer 2

Answer:

Heya

Step-by-step explanation:

given ,

AM , BN & CL are medians  

to prove -ar. ΔAGB = ar.ΔAGC , ar.ΔAGB = ar. ΔBGC & ΔAGB= 1/3ar.ΔABC  

proof ,

in ΔAGB & ΔAGC

 AG is the median  

∴ ar. ΔAGB = ar.ΔAGC

similarly ,

 BG is the median  

∴ ar.ΔAGB = ar. ΔBGC  

so we can say that ar. ΔAGB = ar.ΔAGC =  ΔBGC  

now ,

ΔAGB + ΔAGC + ΔBGC = ar. ΔABC  

1/3ΔAGB +1/3ΔAGC + 1/3ΔBGC ( they are equal in area ) = ar. ΔABC  

so we can say that ,  

ΔAGB = ar.ΔAGC =  ΔBGC = ar 1/3 ΔABC  

  ( PROVED )