As shown in the figure, in square ABCD, ∠ EDF = 45 ° and the two sides of ∠ EDF intersect AB and BC respectively at e and F. try to explore the quantitative relationship between AE, EF and CF, and prove your conclusion

As shown in the figure, in square ABCD, ∠ EDF = 45 ° and the two sides of ∠ EDF intersect AB and BC respectively at e and F. try to explore the quantitative relationship between AE, EF and CF, and prove your conclusion

Reason: as shown in the figure: the Ba to G is extended, so that Ag = CF, connect DG, \\ △ ADG and △ CDF, ad = CD ∈ DAG = C = 90, ad = CD Dang = DAG = C = 90 ° Ag = 90 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\∠ edfde = De, Ψ Δ DGE ≌ △ DFE (SAS), ≌ Ge = EF, and ∵ Ag = CF, ≌ EF = AE + FC