As shown in the figure, the quadrilateral ABCD is a square, △ ADF is rotated to get △ Abe, ∠ 1 = ∠ 2, please judge: (1) the shape of △ AEG; (2) the relationship between Ag and BG + DF

(1) From the properties of rotation, it can be concluded that ∠ EAB = ∠ 1 = ∠ 2, ∠ EAF = 90 °, EB = DF, ∠ EAG = 90 °- ∠ 2, then ∠ e = 90 °- ∠ EAB = 90 °- ∠ 2, ∠ EAG = ∠ e, △ AEG is isosceles triangle; (2) from (1) we can get: EB = DF, then Ag = eg = EB + BG = BG + DF

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