Question

如图在三角形ABC中,∠B=90°,E,F分别在AB,AC上,沿EF对折,使点A落在BC上的点D处,

Answer 1

设CD＝X

∵∠B＝90,∠BAC＝45

∴∠C＝180-∠B-∠BAC＝45

∴AB＝BC

∵FD⊥BC

∴FD∥AB,等腰RT△CDF

∴∠AEF＝∠DFE,DF＝CD＝X,CF＝√2CD＝√2X

∵△AEF沿EF折叠至△DEF

∴EF垂直平分AD,∠AFE＝∠DFE

∴AF＝DF＝X,∠AEF＝∠AFE

∴AE＝AF＝X

∵AC＝AF+CF＝（√2+1）X

∴AB＝AC/√2＝（1+√2/2）X

∴BE＝AB-AE＝√2X/2

∴AE/BE＝X/（√2X/2）＝√2