如图 AD是△ABC的角平分线,AD的垂直平分线交与AB,BC的延长线于点F,E

（1）EF是AD的垂直平分线,故FA=FD,∴∠FDA=∠FAD∵AD是角平分线,∴∠FAD=∠DAC,∴∠FDA=DAC,∴DF‖AC（内错角）（2）EF是AD垂直平分线,所以EA=ED,所以∠EAD=∠EDA∠EAD=∠CAD+∠CAE∠EDA=∠B+∠BAD∵∠CAD=∠BAD∴∠CAE=∠B