Verification: the sum of squares of two diagonals of a parallelogram is equal to the sum of squares of four sides

Known, parallelogram ABCD. Prove: AC & # 178; + BD & # 178; = AB & # 178; + CD & # 178; + AD & # 178; + BC & # 178; prove: as shown in the figure, make AE ⊥ BC, DF ⊥ BC. ∵ ABCD is parallelogram (known) ∥ ad ∥ BC, ad = BC, ab = CD (parallelogram opposite sides are parallel and equal) ≁ AE ⊥ BC, What we do is \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\it's not easy; -2BC·BE+BE²+BE)²+(DF²+BC²+2BC·CF+CF²)=AE²+BE²+BC²+DF²+CF²+BC²=AB²+BC²+CD²+AD

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