Question

state the appolonius theorem ​

Answer 1

In geometry, Apollonius's theorem is a theorem relating the length of a median of a triangle to the lengths of its side. It states that "the sum of the squares of any two sides of any triangle equals twice the square on half the third side, together with twice the square on the median bisecting the third side".

Specifically, in any triangle ABC, if AD is a median, then

{\displaystyle |AB|^{2}+|AC|^{2}=2(|AD|^{2}+|BD|^{2}).} {\displaystyle |AB|^{2}+|AC|^{2}=2(|AD|^{2}+|BD|^{2}).}

It is a special case of Stewart's theorem. For an isosceles triangle with |AB| = |AC|, the median AD is perpendicular to BC and the theorem reduces to the Pythagorean theorem for triangle ADB (or triangle ADC). From the fact that the diagonals of a parallelogram bisect each other, the theorem is equivalent to the parallelogram law.

Answer 2

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