Question

如图10所示,在△ABC中,AB=AC,D是BA延长线上一点,E在AC上,且AD=AE,请问DE与BC有什么位置关系

Answer 1

DE⊥BC.理由：延长DE交BC于F,∵AB=AC,∴∠B=∠C=1/2(180°-∠BAC)=90°-1/2∠BAC,∵AD=AE,∴∠D=∠AED=1/2(180°-∠DAE)=90°-1/2∠DAE,∴∠B+∠D=180°-1/2(∠BAC+∠DAE)=180°-90°=90°,∴∠DFB=90°,∴DE⊥BC.