如图,已知∠1+∠2=180°,∠DEF=∠A,求证:∠ACB=∠DEB.-七年级数学

题目简介

如图,已知∠1+∠2=180°,∠DEF=∠A,求证:∠ACB=∠DEB.-七年级数学

题目详情

如图,已知∠1 +∠2 =180°,∠DEF =∠A,求证:∠ACB = ∠DEB
题型:解答题难度:中档来源:不详

答案

见解析
证明:∵      ∴······ 2分
EFAB·································· 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,从而求得DE∥AC,最后得出结论

更多内容推荐