题型:解答题-证明题
难度:0.4
引用次数:897
题号:16650021
如图1,直线
与直线
分别交于点E、F,
平分
交
于点M,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/30/896c08c6-f249-460d-b4c3-61a15134611f.png?resizew=365)
(1)求证:
;
(2)如图2,点G是射线
上一动点(不与点M、F重合),
平分
交
于点H,
于点N,设
.
①当点G在点F的右侧时,若
,求
的大小;
②点G在整个运动过程中,直接写出
和
之间的数量关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b79c80cc81b5446dfac3ee97b03c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b6a23d521606a35298bbf147f7f830c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f05e8865501e46021ae90fa465bca7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/30/896c08c6-f249-460d-b4c3-61a15134611f.png?resizew=365)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
(2)如图2,点G是射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2e2c0d4ac2bd79f6cea7a9b1a50662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589786dd7c3a2679c3230b671cd232d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d335bf8cb2e6e5e50d0e03a14d1f48d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6df8f48e27453face64d3ae6b766f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8337d8a7098fffd6a01ee270825469f.png)
①当点G在点F的右侧时,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa6bd1caf4f87388261fafbdf3f3684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
②点G在整个运动过程中,直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
更新时间:2022-08-29 12:21:22
|
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解答题-证明题
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解题方法
【推荐1】如图,直线
,一副直角三角板
中,
.
(1)若
如图1摆放,当
平分
时,证明:
平分
.
![](https://img.xkw.com/dksih/QBM/2021/6/24/2749989974278144/2776266230341632/STEM/fd40c06b-2fff-48d4-a708-9c4fc0b19545.png)
(2)若
如图2摆放时,则
![](https://img.xkw.com/dksih/QBM/2021/6/24/2749989974278144/2776266230341632/STEM/875ee310-c2e8-4187-96f0-cbcd8e28f2aa.png)
(3)若图2中
固定,将
沿着
方向平移,边
与直线
相交于点
,作
和
的角平分线
相交于点
(如图3),求
的度数.
![](https://img.xkw.com/dksih/QBM/2021/6/24/2749989974278144/2776266230341632/STEM/9682e942-b2e5-46f5-8436-a19e1e4616e7.png)
(4)若图2中
的周长
,现将
固定,将
沿着
方向平移至点
与
重合,平移后的得到
,点
的对应点分别是
,请直接写出四边形
的周长.
(5)若图2中
固定,(如图4)将
绕点
顺时针旋转,
分钟转半圈,旋转至
与直线
首次重合的过程中,当线段
与
的一条边平行时,请直接写出旋转的时间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0418e1c2453e13f6b51ae58543be592f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d9b8cc71ba241595722780e24cdad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b313af9d797163ba8fcc698f8a35ca4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3634979dfcebf857b20874dd320d80b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44522c4d17b8a92313252c972f48ef46.png)
![](https://img.xkw.com/dksih/QBM/2021/6/24/2749989974278144/2776266230341632/STEM/fd40c06b-2fff-48d4-a708-9c4fc0b19545.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d9b8cc71ba241595722780e24cdad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa4b70236c2d6820cc3859c52c97d9b.png)
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(3)若图2中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3634979dfcebf857b20874dd320d80b3.png)
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(4)若图2中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3634979dfcebf857b20874dd320d80b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9598a6e29b664bf6a631d4d2d2051b7.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1884f6ded12ef8d47ee61c2b618244b.png)
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(5)若图2中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3634979dfcebf857b20874dd320d80b3.png)
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解答题-问答题
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解题方法
【推荐2】一副三角尺(分别含∠B=∠AOB=45°,∠A=90°和∠D=30°,∠COD=60°,∠C=90°)按如图所示摆放使得B、O、D三点共线.将三角尺ABO绕点O以每秒4°的速度顺时针旋转,当边AO与OD重合时停止运动,设三角尺ABO的运动时间为t秒.
![](https://img.xkw.com/dksih/QBM/2022/2/7/2911106839683072/2918393043222528/STEM/256fc1e3-c845-4131-ad82-97b068147841.png?resizew=351)
(1)当t=10时,∠AOD= °.
(2)求出当t为何值时,边AO平分∠COD.
(3)若在三角尺ABO开始旋转的同时,三角尺OCD也绕点O以每秒1°的速度逆时针旋转,当三角尺ABO停止旋转时,三角尺OCD也停止旋转.在旋转过程中,是否存在某一时刻使∠AOD=2∠BOC,若存在,请直接写出t的值;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/2022/2/7/2911106839683072/2918393043222528/STEM/256fc1e3-c845-4131-ad82-97b068147841.png?resizew=351)
(1)当t=10时,∠AOD= °.
(2)求出当t为何值时,边AO平分∠COD.
(3)若在三角尺ABO开始旋转的同时,三角尺OCD也绕点O以每秒1°的速度逆时针旋转,当三角尺ABO停止旋转时,三角尺OCD也停止旋转.在旋转过程中,是否存在某一时刻使∠AOD=2∠BOC,若存在,请直接写出t的值;若不存在,请说明理由.
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【推荐3】已知O为直线AB上一点,∠COE是直角,OF平分∠AOE.
(1)如图①,若∠COF=34°,则∠BOE=________;若∠COF=n°,则∠BOE=________;∠BOE与∠COF的数量关系为________________.
(2)当射线OE绕点O逆时针旋转到如图②的位置时,(1)中∠BOE与∠COF的数量关系是否仍然成立?请说明理由.
(3)在图③中,若∠COF=65°,在∠BOE的内部是否存在一条射线OD,使得2∠BOD与∠AOF的和等于∠BOE与∠BOD的差的一半?若存在,请求出∠BOD的度数;若不存在,请说明理由.
(1)如图①,若∠COF=34°,则∠BOE=________;若∠COF=n°,则∠BOE=________;∠BOE与∠COF的数量关系为________________.
(2)当射线OE绕点O逆时针旋转到如图②的位置时,(1)中∠BOE与∠COF的数量关系是否仍然成立?请说明理由.
(3)在图③中,若∠COF=65°,在∠BOE的内部是否存在一条射线OD,使得2∠BOD与∠AOF的和等于∠BOE与∠BOD的差的一半?若存在,请求出∠BOD的度数;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/2018/8/27/2019462946791424/2019713526259712/STEM/f49c5fa578b14eea80e845210ae152a4.png?resizew=403)
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【推荐1】已知AB∥CD,解决下列问题:
(1)如图①,BP、DP分别平分∠ABE、∠CDE,若∠E=100°,求∠P的度数.
(2)如图②,若∠ABP=
∠ABE,∠CDP=
∠CDE,试写出∠P与∠E的数量关系并说明理由.
(3)如图③,若∠ABP=
∠ABE,∠CDP=
∠CDE,设∠E=m°,求∠P的度数(直接用含n、m的代数式表示,不需说明理由).
(1)如图①,BP、DP分别平分∠ABE、∠CDE,若∠E=100°,求∠P的度数.
(2)如图②,若∠ABP=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
(3)如图③,若∠ABP=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee6a2eba56d4f2d1670b0256b8d86b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee6a2eba56d4f2d1670b0256b8d86b92.png)
![](https://img.xkw.com/dksih/QBM/2019/3/15/2161035651489792/2162379907039232/STEM/950fe786c96a4171bce450664804329e.png?resizew=474)
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【推荐2】(1)如图1,AB∥CD,点M为直线AB,CD所确定的平面内的一点,若∠A105,∠M108,请直接写出∠C的度数 ;
(2)如图2,AB∥CD,点P为直线AB,CD所确定的平面内的一点,点E在直线CD上,AN平分∠PAB,射线AN的反向延长线交∠PCE的平分线于M,若∠P30,求∠AMC的度数;
(3)如图3,点P与直线AB,CD在同一平面内,AN平分∠PAB,射线AN的反向延长线交∠PCD的平分线于M,若AMC180
P,求证:AB∥CD.
(2)如图2,AB∥CD,点P为直线AB,CD所确定的平面内的一点,点E在直线CD上,AN平分∠PAB,射线AN的反向延长线交∠PCE的平分线于M,若∠P30,求∠AMC的度数;
(3)如图3,点P与直线AB,CD在同一平面内,AN平分∠PAB,射线AN的反向延长线交∠PCD的平分线于M,若AMC180
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
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