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如图,在Rt△ABC中,∠ACB=90°,点D、E分别是AB、BC的...
(1)证明:∵∠ACB=90°,点D是AB的中点,∴CD=BD,∴∠B=∠DCE,∵∠FEC=∠B,∴∠FEC=∠DCE,∵点E是BC的中点,∴∠CED=90°,∴∠CED=∠ECF=90°,在△CDE和△...
...为EF的中点.求证:(1)△BDE≌△CFD;(2)DG⊥EF.
(1)在△ABC中,AB=AC,∴∠B=∠C,∵BD=CF,CD=BE,∴△BDE≌△CFD,∴DE=DF.(2)由(1)知DE=DF,即△DEF是等腰三角形,∵G为EF的中点,∴DG⊥EF.