Question

如圖，已知∠1 +∠2 =180°，∠DEF =∠A，求證：∠ACB = ∠DEB．

Answer 1

見解析

證明：∵ ，     ∴······ 2分
∴ EF∥AB·································· 3分
∴ ∠DEF =∠BDE······························· 4分
∵ ∠DEF=∠A
∴ ∠BDE =∠A································ 6分
∴ DE∥AC·································· 7分
∴ ∠ACB =∠DEB 8分
利用平角可求得EF∥AB，從而求得DE∥AC，最后得出結論