In the parallelogram ABCD, AC and BD are diagonals, the proof is: AC & # 178; + BD & # 178; = AB & # 178; + BC & # 178; + CD & # 178; + Da & # 178;

In the parallelogram ABCD, AC and BD are diagonals, the proof is: AC & # 178; + BD & # 178; = AB & # 178; + BC & # 178; + CD & # 178; + Da & # 178;

Then, be = CF, so EF = BC, AC ^ 2 = AE ^ 2 + (bc-be) ^ 2, BD ^ 2 = DF ^ 2 + (BC + CF) ^ 2, because AE = DF, be = CF, so AC ^ 2 + BD ^ 2 = 2ae ^ 2 + 2BC ^ 2 + 2be ^ 2 = 2 (AE ^ 2 + be ^ 2) + 2BC ^ 2 = 2Ab ^ 2 + 2BC ^ 2 = 2 (AB ^ 2 + BC ^ 2)