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`        If G is the centroid of a triangle ABC, then , prove analytically that ∆BCG= ∆CAG= ∆ABG`
2 years ago

Arun
23340 Points
```							We know that, the median of a triangle divide it into two triangles of equal area.In ΔABC, AD is the median∴ ar (ΔABD) = ar (ΔACD)   ...(1)In ΔGBC, GD is the median.∴ ar(ΔGBD) = ar(ΔGCD)   ...(2)Subtracting (2) from (1), we getar(ΔABD) – ar(ΔGBD) = ar(ΔACD) – ar(ΔGCD)∴ ar(ΔAGB) = ar(ΔAGC) ...(3)Similarly, ar(ΔAGB) = ar(ΔBGC)   ...(4)From (3) and (4), we getar(ΔAGB) = ar(ΔAGC) = ar(ΔBGC)   ...(5)Now, ar(ΔAGB) + ar(ΔAGC) + ar(ΔBGC) = ar(ΔABC)⇒ ar(ΔAGB) + ar(ΔAGB) + ar(ΔAGB) = ar(ΔABC)   (Using (5))⇒ 3ar(ΔAGB) = ar(ΔABC)⇒ ar(ΔAGB) .......(6)From (5) and (6), we getar(ΔAGB) = ar (ΔAGC) = ar(ΔBGC)
```
2 years ago
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• Mind Map
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