For the proof of string theorem: the sum of squares of two diagonals of a parallelogram is equal to the sum of squares of its sides

For the proof of string theorem: the sum of squares of two diagonals of a parallelogram is equal to the sum of squares of its sides

How to say it? You first draw a parallelogram with width a and length B, and then connect the diagonal m (longer bar) and N, and the angle a (larger angle}), B (both are mathematical slogans, which are expressed by ● below. They are complementary). Prove that: as shown in the figure, let the parallelogram have width a and length B, and the diagonal m and N respectively. Then M "= a" + B "- 2abcos}, n" = a "+ B" - 2abcos ‰, so the sum of squares of the diagonal m "+ n" = (the above two expressions are combined, And because cos} = cos (180 - ×) = - cos ×, so m "+ n" = 2 (a "+ B"), so (the conclusion to be proved) "the sign of square, if it is OK,

Prove that the sum of squares of four sides of a parallelogram is equal to the sum of squares of diagonals
Parallelogram oabc
OB^2+AC^2=OA^2+AB^2+BC^2+CO^2

If the side length of a diamond is 3, what is the sum of the squares of the two diagonals of the diamond

Let two diagonals be x and Y respectively. By using Pythagorean theorem, we can get (x / 2) & sup2; + (Y / 2) & sup2; = 3 & sup2;, X & sup2; + Y & sup2; = 36