如图,点E在直线DF上,点B在直线AC上,若∠1=∠2,∠3=∠4,则∠A=∠F,请说明理由.
解:∵∠1=∠2(已知)
∠2=∠DGF{#blank#}1{#/blank#}
∴∠1=∠DGF
∴BD∥CE{#blank#}2{#/blank#}
∴∠3+∠C=180°{#blank#}3{#/blank#}
又∵∠3=∠4(已知)
∴∠4+∠C=180°
∴{#blank#}4{#/blank#} ∥{#blank#}5{#/blank#}(同旁内角互补,两直线平行)
∴∠A=∠F{#blank#}6{#/blank#} .
![](http://tikupic.21cnjy.com/86/3c/863cf0c8000263c67a58e2da4b1278a1.png)