如图,在△ABC中,∠A=90°,AB=AC,∠ABC的平分线BD交AC于D,CE⊥BD的延长线于点E.求证:CE=1/2BD.

问题描述:

如图,在△ABC中,∠A=90°,AB=AC,∠ABC的平分线BD交AC于D,CE⊥BD的延长线于点E.求证:CE=

1
2
BD.

延长CE、BA相交于点F.∵∠EBF+∠F=90°,∠ACF+∠F=90°∴∠EBF=∠ACF.在△ABD和△ACF中∠EBF=∠ACFAB=AC∠BAC=∠CAF∴△ABD≌△ACF(ASA)∴BD=CF在△BCE和△BFE中∠EBF=∠CBEBE=BE∠CEB=∠FEB,∴△BCE≌...