如图,已知直线AB与CD相交于点O,OE⊥AB,OF⊥CD,OM是∠BOF的角平分线
(1)若∠AOC=25°,求∠BOD和∠COE的度数.
(2)若∠AOC=α,求∠EOM的度数(用含α的代数式表示)
(1)若∠AOC=25°,求∠BOD和∠COE的度数.
(2)若∠AOC=α,求∠EOM的度数(用含α的代数式表示)
![](https://img.xkw.com/dksih/QBM/2019/3/26/2168922449502208/2170969718587393/STEM/a99d1ca28c434892b1a8712be5d5eb02.png?resizew=199)
更新时间:2019-03-29 15:52:06
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解答题-证明题
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适中
(0.65)
【推荐1】如图,在△
中,
,
,
,
,
与
相交于点
.
![](https://img.xkw.com/dksih/QBM/2022/3/1/2926848392372224/3028721719238656/STEM/d08b2cdf838349c1ba3a1420060fbd37.png?resizew=147)
(1)求∠BOC的度数;
(2)求证:△ABC为等边三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b8b98b2f83279a49e94d9f48c5e6f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49c8dbc31b2e14067ef2f34b4e25f114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70734a8e672376bb0bd1522e229f86a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f913298f0fae9f55377a8deab9f099dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/2022/3/1/2926848392372224/3028721719238656/STEM/d08b2cdf838349c1ba3a1420060fbd37.png?resizew=147)
(1)求∠BOC的度数;
(2)求证:△ABC为等边三角形.
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解答题-证明题
|
适中
(0.65)
【推荐2】阅读并完成下面的证明过程:
已知:如图
分别平分
和
.
求证:
.
证明:∵
、
分别平分
和
.
∴
,
___________
(角平分线定义)
又∵![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e53497af8899cb299d762f1a4f46a55.png)
∴
( )
∴
(___________)
又∵
(已知)
∴
( )
∴
( )
∴![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293d1222b936b48696ad157c6936f8f8.png)
又∵![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0782b64e9a9e02436620c9421b32d6c2.png)
∴
( )
∴![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb1fd3973d683ae0dc166a7bcea7bb8d.png)
∴![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f46f19939f38833f9152942f8241b7c.png)
∴
( )
已知:如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d340fcfe97100c7e9ae0d111f27a42f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727ad3e630a224303d6d3b8ad5c114ba.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31b2cc1d0bfd22c88286880b9da1f6f4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/23/41daaf73-4398-4093-beeb-256b2530bd3e.png?resizew=130)
证明:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727ad3e630a224303d6d3b8ad5c114ba.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ec6dfd990e1da5001d0a881fbe90db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc310194575262fb45352c2fbc19868.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e709e345ae78ecfd2b169873d3b52e3.png)
又∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e53497af8899cb299d762f1a4f46a55.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d4d34c3629c2f7cacadfe730093b68.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b4d919cf7b4b11ac9fb88abf47a323.png)
又∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0782b64e9a9e02436620c9421b32d6c2.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08d61b3755919715a278c5147fa4514c.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293d1222b936b48696ad157c6936f8f8.png)
又∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0782b64e9a9e02436620c9421b32d6c2.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265bb9bf310e6bcae723c61ff91e26ec.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb1fd3973d683ae0dc166a7bcea7bb8d.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f46f19939f38833f9152942f8241b7c.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31b2cc1d0bfd22c88286880b9da1f6f4.png)
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