In Delta ABC,if ldots ldots ldots ldots,then | vedclass

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(A) Apollonius' theorem states that for any triangle $\Delta ABC$,if $\overline{AD}$ is the median to the side $\overline{BC}$,then the sum of the squ

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$\overline{AD}$ is a median

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(A) Apollonius' theorem states that for any triangle $\Delta ABC$,if $\overline{AD}$ is the median to the side $\overline{BC}$,then 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 side bisected by the median.Mathematically,this is expressed as $AB^{2} + AC^{2} = 2(AD^{2} + BD^{2})$,where $BD = DC = \frac{1}{2}BC$.Comparing this with the given equation $AB^{2} + AC^{2} = 2(AD^{2} + BD^{2})$,it is clear that $\overline{AD}$ must be the median to side $\overline{BC}$.

In $\Delta ABC$,if $\ldots \ldots \ldots \ldots$,then by Apollonius' theorem,$AB^{2} + AC^{2} = 2(AD^{2} + BD^{2})$ holds good.

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