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于点F,下列结论1.∠BIC=90°+1/2∠BAC2.图中与∠EIB互余的角有3个3.2∠AIB=∠ABC+∠FIC+∠BAC4.∠BID=∠CIE.其中正确的结
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![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于点F,下列结论1.∠BIC=90°+1/2∠BAC2.图中与∠EIB互余的角有3个3.2∠AIB=∠ABC+∠FIC+∠BAC4.∠BID=∠CIE.其中正确的结](/uploads/image/z/10157953-49-3.jpg?t=%E5%A6%82%E5%9B%BE%2C%E2%96%B3ABC%E7%9A%84%E4%B8%89%E6%9D%A1%E8%A7%92%E5%B9%B3%E5%88%86%E7%BA%BF%E4%BA%A4%E4%BA%8EI%E7%82%B9%28%E2%88%A0ACB%3E%E2%88%A0ABC%29%2CAI%E4%BD%9CIE%E2%8A%A5BC%E4%BA%8ED%2C%E4%BD%9CIE%E2%8A%A5BC%E4%BA%8EE%2C%E4%BD%9CIF%E2%88%A5AB%E4%BA%A4BC%E4%BA%8E%E7%82%B9F%2C%E4%B8%8B%E5%88%97%E7%BB%93%E8%AE%BA1.%E2%88%A0BIC%3D90%C2%B0%2B1%2F2%E2%88%A0BAC2.%E5%9B%BE%E4%B8%AD%E4%B8%8E%E2%88%A0EIB%E4%BA%92%E4%BD%99%E7%9A%84%E8%A7%92%E6%9C%893%E4%B8%AA3.2%E2%88%A0AIB%3D%E2%88%A0ABC%2B%E2%88%A0FIC%2B%E2%88%A0BAC4.%E2%88%A0BID%3D%E2%88%A0CIE.%E5%85%B6%E4%B8%AD%E6%AD%A3%E7%A1%AE%E7%9A%84%E7%BB%93)
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于点F,下列结论1.∠BIC=90°+1/2∠BAC2.图中与∠EIB互余的角有3个3.2∠AIB=∠ABC+∠FIC+∠BAC4.∠BID=∠CIE.其中正确的结
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于点F,下列结论
1.∠BIC=90°+1/2∠BAC
2.图中与∠EIB互余的角有3个
3.2∠AIB=∠ABC+∠FIC+∠BAC
4.∠BID=∠CIE.其中正确的结论是?
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于点F,下列结论1.∠BIC=90°+1/2∠BAC2.图中与∠EIB互余的角有3个3.2∠AIB=∠ABC+∠FIC+∠BAC4.∠BID=∠CIE.其中正确的结
(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