BE评分∠B,EF⊥BC,EA⊥BA=>EF=EA ∴ Rt△BAE≌Rt△BFE（HL) =>BA=BF =>∠AEB=∠FEB,EF=EA,EG=EG=>△AEG≌△FEG(SAS) =>GA=GF,∵BA=BF,BG=BG
=>△BGA≌△BGF(SSS) =>∠BAE=∠BFG,∵∠BAE=∠C,∴∠BFG=∠C =>GF//AE---(1)
EF⊥BC,EA⊥BA =>EF//AG---(2)
(1)(2) =>□AEFG,∵EF=EA => 四边形AEFG是菱形