Question

如图,△ABC的三条角平分线交于I点(∠ACB>∠ABC),AI作IE⊥BC于D,作IE⊥BC于E,作IF∥AB交BC于

Answer 1

(1)正确,角BIC=180度-IBC-ICB=180-1/2ABC-1/2ACB=90度+1/2(180度-ABC-ACB)=90度+1/2BAC

(2)正确,角FIB=IBA=IBC都与EIB互余

(3)不正确,

举反例,

当角ABC=50度,角ACB=60度,角BAC=70度时,

有角AIB=120度,2角AIB=240度,

FIC=180度-ICB-IFC=180度-ICB-CBA=100度,

角ABC+FIC+BAC=50+100+60=210度

(4)正确,角BID=IBA+IAB=1/2(ABC+CAB)=1/2(180度-BCA)=90度-1/2BCA=90度-ICA=CIE