Question

BD是△ABC的角平分线,BD的垂直平分线交CA的延长线于点E,求证角EAB=角EBC

Answer 1

EF是BD的垂直平分线

∴ △EBG≌△EDG
∠EDB=∠EBD
∵∠EDB=∠C+∠CBD
∴∠EBD=∠C+∠CBD
BD平分∠ABC,∴∠ABD=∠CBD
∵∠EBD=∠EBA+∠ABD
∴∠EBD=∠EBA+∠CBD
∴∠C+∠CBD=∠EBA+∠CBD
∴∠C=∠EBA
∵∠EAB=∠C+∠ABC
∴∠EAB=∠EBA+∠ABC=∠EBC