Question

在三角形abc中,角abc=角eaf=90°,ab=ac,ae=af

Answer 1

1, ∠EFB=90 ∠FBE=∠FEB=45 EF=BF

∠AEB=90

AE^2=EF^2/2=BF^2/2 EB^2=2BF^2

AE^2+EB^2=AB^2

BF^2/2+2BF^2=AB^2

5BF^2=2AB^2

AB:BF=√5:√2

2, ∠EBF=90 ∠EFB=∠FEB=45 BE=BF

∠AEB=∠AFB=45+45=90 AE=AF 四边形AEBF为正方形

AB：BF=√2：1

3,∠FEB=90 ∠EFB=∠EBF=45 EF=EB

∠AFB=45+45=90

AF^2=EF^2/2 BF=2EF^2 AF^2+BF^2=AB^2

EF^2/2+2EF^2=AB^2

5EF^2=2AB^2 EF^2=BF^2/2

5BF^2=4AB^2

AB:BF=√5:2