Question

如图,已知在△ABC中,AD平分角BAC,EF垂直平分AD,求证角B=角CAE

Answer 1

∵EF垂直平分AD

∴EA=ED

∴∠EAD＝∠EDA

∵AD平分角BAC,即∠BAD＝∠CAD

又∵∠EDA=∠B+∠BAD; ∠EAD＝∠CAE＋∠CAD

∴∠B=∠EDA－∠BAD=∠EAD-∠CAD=∠CAE