如题所述
证明:过E做EG//AD ,交AC于G ,连接E、E‘
四边形AGEE’ 为平行四边形,AE'=EG
∵ ∠CGE =∠A ∠A =90 -∠ACD ∠CDE =90 -∠ACD
∴ ∠CGE =∠CDE
∵ ∠ECD =∠ECG CE=CE
∴ △ECD ≌ △ECG
DE=EG
∵ ∠CFD = 90 -∠DCF = 90 -∠BCE ∠DEF =∠BEC = 90 -∠BCE
∴ ∠CFD =∠DEF
DF=DE
∵ AE'=EG EG=DE
∴ AE' = DF