In square ABCD, AE = ed, BF = FC, we prove that 1. All △ Abe is equal to △ CDF. 2. A quadrilateral bfde is a parallelogram

1 AE = ed = ad / 2BF = FC = BC / 2, so AE = CF and ab = CD be = under the root sign (AB & # 178; + AE & # 178;) = under the root sign (CD & # 178; + CF & # 178;) = DF, so △ Abe ≌ △ CdF2 BF = BC / 2 = ad / 2 = de and ad ∥ BC, so a group of parallelograms with opposite sides parallel and equal are parallelograms

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