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Prove that three times the sum of the sq...

Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle.

Answer

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Knowledge Check

  • Read the statemenst carefully and state 'T' for true and 'F' for false . 1. If a line divides any two sides of a triangle in the same ratio , then the line is parallel to the third side of the triangle . 2 . The internal bisector of an angle of a triangle divides the opposite side inernally in the ratio of the sides containing the angle . 3 . If a line through one vertex of a triangle divides the opposite in the ratio of other two sides , then the line bisects the angle at the vertex . 4.Any line parallel to the parallel sides dividesproportionally . 5. Two times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle .

    A
    `{:(1,2,3,4,5),(T,T,T,T,T):}`
    B
    `{:(1,2,3,4,5),(T,T,T,T,F):}`
    C
    `{:(1,2,3,4,5),(F,T,F,T,F):}`
    D
    `{:(1,2,3,4,5),(T,T,F,T,F):}`

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