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The parallelogram law of vector addition states that if two vectors are considered to be the two adjacent sides of a parallelogram with their tails meeting at the common point, then the diagonal of the parallelogram originating from the common point will be the resultant vector.
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The Parallelogram law states that the sum of the squares of the length of the four sides of a parallelogram is equal to the sum of the squares of the length of the two diagonals. In Euclidean geometry, it is necessary that the parallelogram should have equal opposite sides. 2(AB)2 + 2 (BC)2 = (AC)2 + (BD)2
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