As shown in the figure, we know that the parallelogram ABCD and AC BD are diagonals, and prove that AC & # 178; + BD & # 178; = 2 (AB & # 178; + BC & # 178;)

For abd, ABC uses two cosine theorems: BD & # 178; = AB & # 178; + AD & # 178; - 2 ab ad cos AAC & # 178; = AB & # 178; + BC & # 178; - 2 ab BC cos B = AB & # 178; + BC & # 178; - 2 ab ad cos (180-a) = AB & # 178; + BC & # 178; + 2 ab ad cos a

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1. In the parallelogram ABCD, it is known that the lengths of two diagonal lines AC and BD are 4 and 6 respectively, then AB & # 178; + BC & # 178=
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