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Prove that If the medians of a A B C in...

Prove that If the medians of a ` A B C` intersect at `G ,` show that `a r( A G B)=a r( A G C)=a r( B G C)=1/3a r( A B C)`

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Verified by Experts

`In/_ABC`, AD is median
`ar(/_ABD)=ar(/_ACD)-(1)`
`In/_GBC`,GD is median
`ar(/_GBD)=ar(/_GCD)-(2)`
subtracting equation 2 from 1
`ar(/_ABG)=ar(/_ACG)-(3)`
`ar(/_AGB)=ar(/_BGC)-(4)`
`ar(/_ABG)=ar(/_BGC)=ar(/_AC C_1)`
...
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