Question

如图,AD是三角形ABC的角平分线,AD的垂直平分线交AB于点F,交BC的延长线于点E.求证：∠CAE=∠B

Answer 1

假设EF与AD交于H点,x0d因为EF垂直于AD ,所以x0d∠CAE ∠DAC ∠AEF=90x0d因为AD是∠BAB平分线,∠DAC=∠BADx0d∠ADC ∠DEF=90 因为EF垂直于AD并平分AD ,所以∠DEF=∠AEF ∠CAE ∠DAC ∠AEF=90 ∠ADC ∠DEF=90x0d∠DEF=∠AEF