國二數學問題急急急?拜託!!?

2020-12-06 9:55 am
∆ABC、∆ADE中,C、D兩點分別在AE、AB上,BC與DE相交於F點。若BD=CD=CE,∠A=66∘,∠B=40∘,請說明DF>CF的理由???

回答 (1)

2020-12-06 11:13 am
✔ 最佳答案
BD = CD,
∴ ∠B = ∠DCB
CD = CE
∴ ∠E = ∠CDE

∠A = 66°, ∠B = 40°
∴ ∠BCA = 74°
∴ ∠DCA = ∠BCA - ∠DCB
         = 74°-40° = 34°
   ∠ADC = 180° - 34° - 66° = 80°

   ∠A + ∠ADE + ∠E = 180°
      = ∠A + ∠ADC + ∠CDE + ∠E
      = 66° + 80° + 2∠E
∴ ∠CDE = ∠E
      = (180°-66°-80°)/2 = 17°

△DCF 中, ∠CDF = 17° < ∠DCF = 40°
大角對大邊, ∴ DF > CF


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