如图所示的格线彼此平行
.小明在格线中作
,并探究角之间的数量关系.
,作出
,当
时,
________
;(注:
、
是角的两边与格线所成的角)
(2)如图2,他又在两条格线之间取一点
,作出
,请探究
、
与
之间的数量关系,并证明;(注:
、
是角的两边与格线所成的角)
(3)如图3,点
、
、
、
在格线上,点
在格线之间,
平分
,
平分
,若
,则
________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ade0acee0a50caad911093214aa4bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6978615637bd3febf56d23798f65306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90fad339412670cffa37e8a8bacd7fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc310194575262fb45352c2fbc19868.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83873a9d782f2588c5eedbfe73f9bc2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b69d40b75d582c4b8ffa2369af1d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d57899ad4774aed9ccc7bd23db72153.png)
(2)如图2,他又在两条格线之间取一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b69d40b75d582c4b8ffa2369af1d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d57899ad4774aed9ccc7bd23db72153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b69d40b75d582c4b8ffa2369af1d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d57899ad4774aed9ccc7bd23db72153.png)
(3)如图3,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38f82c22dbe17fa2180f596b9395c4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5c3ca226db5d490fa92bb1b7c8deb14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8187b8c0c45e49cdd8cc160bccfc1ced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e84492ffa051fd5f394029361e9dbd0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83873a9d782f2588c5eedbfe73f9bc2f.png)
22-23七年级下·江苏南京·阶段练习 查看更多[3]
江苏省南京市鼓楼区鼓楼实验中学2022-2023学年七年级下学期3月月考数学试题江苏省南京市江宁区竹山中学2023-2024学年七年级下学期3月月考数学模拟试题(已下线)第02讲 探索平行线的性质(2大考点+7种题型+强化训练)-【帮课堂】2023-2024学年七年级数学下册同步学与练(苏科版)
更新时间:2023-06-08 11:16:02
|
相似题推荐
解答题-问答题
|
较难
(0.4)
【推荐1】王老师在数学实验课中组织学生进行操作探究,用一副三角板(分别含
,
,
和
,
,
的角)按如图1所示摆放,边
与
在同一条直线
上(点C与点E重合).
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/a8b2ff16-0deb-4e37-a2dc-fb8ac75f7b24.png?resizew=402)
(1)如图2,将三角板
从图1的位置开始绕点C以每秒
的速度顺时针旋转,当边
与边
重合时停止运动,设三角板
的运动时间为t秒.当t= 时,边
平分
;
(2)在(1)的条件下,在三角板
开始旋转的同时,三角板
也从原有位置开始绕点C以每秒2°的速度逆时针旋转,当三角板
停止旋转时,三角板
也停止旋转.
①当t为何值时,边
平分
;
②在旋转过程中,是否存在某一时刻使
,若存在,直接写出t的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/a8b2ff16-0deb-4e37-a2dc-fb8ac75f7b24.png?resizew=402)
(1)如图2,将三角板
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/741a44528782580d24249e8075b8cd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/300d3ec6447250bb25915ae86873929a.png)
(2)在(1)的条件下,在三角板
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
①当t为何值时,边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/300d3ec6447250bb25915ae86873929a.png)
②在旋转过程中,是否存在某一时刻使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b512efcbf561f42a184c500ba7efbfc.png)
您最近一年使用:0次
解答题-证明题
|
较难
(0.4)
名校
【推荐2】已知直线
,点A、C在直线
上,点B、D在直线
上.
,
,且
,求
的度数;
(2)如图2,若
,
平分
,
,过D点作
交
于F,求证:
;
(3)如图3,若
,直线
和直线
相交于K,点H在直线
上,探究
、
和
之间的数量关系,请直接写出结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966a7257fd3af3a4049844773c611e26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5b4ea605cf0b98e428d071f6be6762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc5fd5af877362b6990617d008b4f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b6edc361583a9fb853b5755a07cd2.png)
(2)如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5b4ea605cf0b98e428d071f6be6762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2366e94fb2543fec40c9fff54abe1099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/755a11be3b49d05b9215f2f8d1f51c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82d0d611eddafc5dbbfa2f480ef34ffa.png)
(3)如图3,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c03366e8ad89bbf52a24243e94646fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c337e4b1f98e4fa86c461365308b65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35adeb057595dd77b0e7cd8801183d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48689c8d5e36b00d476dcfd2ac3d6024.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
【推荐3】【发现】如图1,CE平分∠ACD,AE平分∠BAC.
(1)当∠EAC=∠ACE=45°时,AB与CD的位置关系是______;
当∠EAC=50°,∠ACE=40°时,AB与CD的位置关系是______;
当∠EAC+∠ACE=90°,请判断AB与CD的位置关系并说明理由;
(2)【探究】如图2,AB∥CD,M是AE上一点,∠AEC=90°保持不变,移动顶点E,使CE平分∠MCD,∠BAE与∠MCD存在怎样的数量关系?并说明理由,
(3)【拓展】如图3,AB∥CD,P为线段AC上一定点,Q为直线CD上一动点,且点Q不与点C重合.直接写出∠CPQ+∠CQP与∠BAC的数量关系.
(1)当∠EAC=∠ACE=45°时,AB与CD的位置关系是______;
当∠EAC=50°,∠ACE=40°时,AB与CD的位置关系是______;
当∠EAC+∠ACE=90°,请判断AB与CD的位置关系并说明理由;
(2)【探究】如图2,AB∥CD,M是AE上一点,∠AEC=90°保持不变,移动顶点E,使CE平分∠MCD,∠BAE与∠MCD存在怎样的数量关系?并说明理由,
(3)【拓展】如图3,AB∥CD,P为线段AC上一定点,Q为直线CD上一动点,且点Q不与点C重合.直接写出∠CPQ+∠CQP与∠BAC的数量关系.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/fb9b9bb6-81d9-4ca7-8f6c-3b8e5628c0c3.png?resizew=484)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
名校
【推荐1】从今年开始,“金鸡百花电影节”长期落户厦门,为了主场馆更好的灯光效果,工作人员设计了灯光组进行舞台投射.其中一组灯光如图所示,灯A射线从AM开始顺时针旋转至AN便立即回转,灯B射线从BP开始顺时针旋转至BQ便立即回转,两灯不停交叉投射.若灯A转动的速度是a°/秒,灯B转动的速度是b°/秒,且a、b满足|a-3b|+(a+b-4)2=0.假定舞台前后幕布是平行的,即PQ∥MN,且∠BAN=45°
(1)求a、b的值;
(2)若灯B射线先转动20秒,灯A射线才开始转动,在灯B射线到达BQ之前,A灯转动几秒,两灯的光束互相平行?
(3)如图,两灯同时转动,在灯A射线到达AN之前.若射出的光束交于点C,过C作CD⊥AC交PQ于点D,则在转动过程中,∠BAC与∠BCD的数量关系是否发生变化?若不变,请求出其数量关系;若改变,请说明理由.
![](https://img.xkw.com/dksih/QBM/2017/4/26/1674120696528896/1679735107624960/STEM/87c051b3-196e-4c03-a250-66ac082486e8.png?resizew=479)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
【推荐2】如图1,
,点
为直线
间一点,点E,F分别是直线
上的点,连接
.
,请完善下面的证明过程,并在( )内填写依据.
证明:过点P作直线
,
(已作),
(______),
又
,
(已知)
______,(______)
,
______.
(2)如图2,若
的平分线与
的平分线交于点
.
①【类比探究】试猜想
与
之间的关系,并说明理由;
②【结论运用】若
,求
的度数.
(3)【拓展认知】如图3,直线
,点P,H为直线
间的点,请直接写出
,
,
,
的数量关系:______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b79c80cc81b5446dfac3ee97b03c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b79c80cc81b5446dfac3ee97b03c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e61a0defee32dd7fd4d86310c456917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a19a0383ba99f036177eb8cd03bc709e.png)
证明:过点P作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31307b00524e461b0ad8dfbcdf24bacf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6200ee85c6a6869b0d422a2a1beece.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51156e40b9f3323d978f57a9c9ed3124.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6200ee85c6a6869b0d422a2a1beece.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c1076691fe7717ac3e2ebbf62e818d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60b7c0c47ca327db7be7946f6fd3b5a.png)
(2)如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9b4a78c3b85dafdaec2e4e6dc87bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a09d2d1b9b9d4562d74196cef3e3ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
①【类比探究】试猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfa70e7c9ef8b856b494d370b7d76482.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b858c70410f981ca3e22f791585c7e.png)
②【结论运用】若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bef32bcf227dfba399970dc19d840e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b858c70410f981ca3e22f791585c7e.png)
(3)【拓展认知】如图3,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28d2790a97390935125aa897417f970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9b4a78c3b85dafdaec2e4e6dc87bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e23792bd3812cdd980cbb8302ef42ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46af6534065a00a2201286531735fed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1be5b1f2ec47a8693b7c710924daf72.png)
您最近一年使用:0次