题型:解答题
难度:0.65
引用次数:458
题号:10870580
如图,已知∠A=∠F,∠C=∠D,求证: BD∥CE.
![](https://img.xkw.com/dksih/QBM/2020/7/17/2507409244905472/2507738349789185/STEM/ca663cce95b24248bfc613984bcf3399.png?resizew=214)
更新时间:2020-07-17 11:09:38
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【知识点】 根据平行线判定与性质证明
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解答题-问答题
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适中
(0.65)
【推荐1】如图,已知AE平分∠BAC交BC于点E,AF平分∠CAD交BC的延长线于点F,∠B=64°,∠EAF=58°,试判断AD与BC是否平行.
∴∠BAC=2∠1,∠CAD= ( ).
又∵∠EAF=∠1+∠2=58°,
∴∠BAD=∠BAC+∠CAD
=2(∠1+∠2)
= °(等式性质).
又∵∠B=64°(已知),
∴∠BAD+∠B= °.
∴
( ).
∴∠BAC=2∠1,∠CAD= ( ).
又∵∠EAF=∠1+∠2=58°,
∴∠BAD=∠BAC+∠CAD
=2(∠1+∠2)
= °(等式性质).
又∵∠B=64°(已知),
∴∠BAD+∠B= °.
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
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解答题-证明题
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适中
(0.65)
【推荐2】已知,如图,
,
求证:
.
证明:
______![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
______
______
______![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
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______![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
______![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
______
______
______![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
______
______![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
______
______
即
______![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913b7537e011acfeec11952731351388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70dbc29101d3815db833af7126911063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fa70ddbabb6c00e42a416c54a216db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e53497af8899cb299d762f1a4f46a55.png)
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9538ac3ed272ad28c632970d75fbab6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149a6cce5802dcd31b45514eb7473721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b418405014e0a5ba8958016a41846a33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c3e7bf8a04b3befbf2487f2effa22a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b700fa9aeb1016aa71f76e4b6bb212e.png)
即
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3b1dae128a2e3e13c93ee3a01430d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913b7537e011acfeec11952731351388.png)
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