Used to prove the chord theorem: the sum of squares of two diagonals of a parallelogram is equal to the sum of squares of its sides.

what can I say? First, you draw a parallelogram with a width of a and a length of b, then the diagonal lines are M (longer bars) and N, and the marked angles are A (larger angle ★) and B (both mathematical slogans, which are denoted by ● below and complement each other). Proof: as shown in the figure, let the parallelogram be a width, b length, m and n diagonal respectively. Then m"=a"+b"-2abcos★, n"=a"+b"-2abcos●, so the sum of squares of diagonal lines is m"+n"= (the above two formulas are merged, which I wrote myself), and because cos ★ = cos (180-●) =-cos.