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Prove that in any parallelogram, the sum of the squares of all sides is equal to the sum of the squares of the diagonals.

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Prove that in any parallelogram, the sum of the squares of all sides is equal to the sum of the squares of the diagonals.

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OA2 + OB2 = x12 + y12 + x22 + y22

OA = BC and OB = AC

OA2 + OB2 + OC2 + AC2

= 2(x12 + y12 + x22 + y22)

AB2 = (x2 – x1)2 + (y2 – y1)2

OC2 = (x1 – x2)2 + (y2 – y3)2

OB2 + OC2 = 2(x12 + x22 + y12 + y22)

OA2 + OB2 + AC2 + BC2 = AB2 + OC2

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