精选问答
(2014•江阴市二模)在正方形ABCD中,P为AB的中点,BE⊥PD的延长线于点E,连接AE、BE、FA⊥AE交DP于点F,连接BF,FC.下列结论:①△ABE≌△ADF;  ②FB=AB;③CF⊥DP;④FC=EF  其中正确的是(  )A.①②④B.①③④C.①②③D.①②③④

2019-12-16

(2014•江阴市二模)在正方形ABCD中,P为AB的中点,BE⊥PD的延长线于点E,连接AE、BE、FA⊥AE交DP于点F,连接BF,FC.下列结论:①△ABE≌△ADF;  ②FB=AB;③CF⊥DP;④FC=EF  
其中正确的是(  )

A.①②④
B.①③④
C.①②③
D.①②③④
优质解答
∵正方形ABCD,BE⊥ED,EA⊥FA,∴AB=AD=CD=BC,∠BAD=∠EAF=∠90°=∠BEF,∵∠APD=∠EPB,∴∠EAB=∠DAF,∠EBA=∠ADP,∵AB=AD,∴△ABE≌△ADF,∴①正确;∴AE=AF,BE=DF,∴∠AEF=∠AFE=45°,取EF的中点M,连... ∵正方形ABCD,BE⊥ED,EA⊥FA,∴AB=AD=CD=BC,∠BAD=∠EAF=∠90°=∠BEF,∵∠APD=∠EPB,∴∠EAB=∠DAF,∠EBA=∠ADP,∵AB=AD,∴△ABE≌△ADF,∴①正确;∴AE=AF,BE=DF,∴∠AEF=∠AFE=45°,取EF的中点M,连...
相关问答