如图，已知ABCD是平行四边形，AE平分∠BAD，CF平分∠BCD，分别交BC、AD于E、F．求证：AF=EC．_刷题宝

题干

如图，已知ABCD是平行四边形，AE平分∠BAD，CF平分∠BCD，分别交BC、AD于E、F．求证：AF=EC．

上一题下一题 0.0难度选择题更新时间:2019-05-28 05:22:41

答案(点此获取答案解析）

证明：∵四边形ABCD是平行四边形，

∴∠B=∠D，AD=BC，AB=CD，∠BAD=∠BCD，

∵AE平分∠BAD，CF平分∠BCD，

∴∠EAB=

1

2

∠BAD，∠FCD=

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