Current location - Education and Training Encyclopedia - Educational institution - As shown in the figure, AB is known to be parallel to CD. ∠EAF= one third ∠EAB∠ECF = one third ∠ECD. Please explain ∠AFC= two thirds ∠AEC.
As shown in the figure, AB is known to be parallel to CD. ∠EAF= one third ∠EAB∠ECF = one third ∠ECD. Please explain ∠AFC= two thirds ∠AEC.
Make GH intersection e parallel to CD, PQ intersection f parallel to AB,

∴∠ECD=∠GEC,∠BAE=∠AEG

∠BAF=∠AFP,∠FCD=∠PFC

∠∠EAF = 1/3∠EAB,∠ECF= 1/3∠ECD

∴2∠EAF=∠FAB,2∠ECF=∠FCD

∴∠aec=∠aeg+∠gec=∠bae+∠ecd=3(∠fae+∠fce)

∠∠AFC =∠AFP+∠CFP =∠BAF+∠DCF = 2(∠EAF+∠ECF)

∴∠AFC=2/3×3(∠FAE+∠FCE)=2/3∠AEC

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