In Delta ABC,overline{AD} is a median. Then,b | vedclass

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(C) Apollonius' theorem states that for any triangle $\Delta ABC$ with median $\overline{AD}$ to side $\overline{BC}$,the sum of the squares of the tw

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$AB^2 + AC^2 = 2(AD^2 + DC^2)$

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(C) Apollonius' theorem states that for any triangle $\Delta ABC$ with median $\overline{AD}$ to side $\overline{BC}$,the sum of the squares of the two sides is equal to twice the sum of the square of the median and the square of half the third side.Mathematically,this is expressed as: $AB^2 + AC^2 = 2(AD^2 + BD^2)$.Since $\overline{AD}$ is a median,$D$ is the midpoint of $\overline{BC}$,so $BD = DC$.Substituting $DC$ for $BD$,we get $AB^2 + AC^2 = 2(AD^2 + DC^2)$.

In $\Delta ABC$,$\overline{AD}$ is a median. Then,by Apollonius' theorem,$\ldots \ldots \ldots \ldots$ holds good.

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