2024六年级下·上海·专题练习
1 . 如图,使用圆规和直尺分别画出
和
的角平分线
和
,如果
,那么:
、
;
(2)写出
的度数___________.
(3)反向延长
到
,写出与
互补的角:___________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22df2977de56cc69be0c1e847653d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b78308c08f97a465ad608e284ed4afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fed1f57a835af4e9022e27603d12d31.png)
(3)反向延长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955c43457ada30fd2b01d2c058a43d7a.png)
您最近一年使用:0次
2 . 如图,A,O,B三点在同一条直线上,
.
的补角是 ,
的余角是 ;
(2)如果
平分
,
,求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d95a92fcd0cd5e55f1d32d42504a5690.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e7b8a59f8d66176463f3d71f882a26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf7a961a55aa7f225fadb6a25a60c75.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22df2977de56cc69be0c1e847653d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfda57590d53444173b20c3c05562c31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/418ebb89d29f4f631b055c911e8d178a.png)
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3 . 如图,直线
相与
相交于O,
分别是
,
平分线.
的两个补角;
(2)若
.求
和
的度数;
(3)试问射线
与
之间有什么特殊的位置关系?为什么?
![](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/5faca03dd3d2b7cc37f4c7c3aad7783e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/418ebb89d29f4f631b055c911e8d178a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7307ac7510cf35f74337d368b94da4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbee6d5731d6f4bb1e4f2ba3d89b7dc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc8e171ac85cbccc8223a0cb5bc8bde3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22df2977de56cc69be0c1e847653d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b2557547eecdc826b8282058802d217.png)
(3)试问射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
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4 . 如图,已知
,
,垂足分别为点G、D,
.
,则
______°;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaa106172cc7b3db22ebbcbc1fe84c04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3575fac382d25eef71830315b2481037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/003664f97a516cca542fd6d82238410f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee2ef38925946da1145a68651da67da9.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e53497af8899cb299d762f1a4f46a55.png)
您最近一年使用:0次
2024-04-27更新
|
31次组卷
|
2卷引用:广东省韶关市翁源县2023-2024学年七年级下学期期中数学试题
5 . 【图形感知】
如图1,
,点
在直线
上,点
在直线
上,点
为
、
之间一点.
,它可以通过如下方法证明,请你帮忙完成该结论的推理过程.
证明:如图①,过点
作
,
∵
,
(已知),
∴
_________(平行于同一条直线的两条直线平行),
∴
,
,
∴
(等式性质)
∴
.
(2)如图3,该基本图形称为“
型”(实线部分),仿照上面结论的推理思路可得
、
、
之间的关系是________;
(3)如图4,直线
,点
,
在直线
上,点
,
在直线
上,直线
,
分别平分
,
,且交于点
.猜想并证明
与
的数量关系.
(4)如图5,已知
,
与
两个角的角平分线相交于点
.
若
,
,设
,
________
.(用含有
,
的代数式表示)
如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/198718d123eb1f8f988d2e04b01dfe55.png)
证明:如图①,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00604947c63f9a8820c17ed3119827d5.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00604947c63f9a8820c17ed3119827d5.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1a378a3a4660eb1ece52085a9b44d5.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de96d1491567868c54a5fd276489deed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08294498984a4056300001478610df24.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8725ac7692814a340c81577f19777b76.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/198718d123eb1f8f988d2e04b01dfe55.png)
(2)如图3,该基本图形称为“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bcdd8c05cd04f46c6f4ba8aa3cb1d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9b4a78c3b85dafdaec2e4e6dc87bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431bd1ab475f5c7936a3b45b317abe99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfa70e7c9ef8b856b494d370b7d76482.png)
(3)如图4,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a4352562ae8aa968014fd0d931b677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdb8eca20ce2c918ea4034ea15210c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246a86f34603eaf2e6a948681b831b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/936f5f26aac7197d42a41081fb1fda0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90026b96116424a245b335b1adb886b.png)
(4)如图5,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eefb9a7a779b6c8d21187ee751c420a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9444b698d7c072a1bc3d46485cb2f92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c86fc02d6dd49a04ad18240e24e91d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30f982ff032e9e6a117987301c1ed1a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e71b29260539127707d057749325e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd00540dba9c02cf78f01abd08db7cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83873a9d782f2588c5eedbfe73f9bc2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
6 . 数学课上,老师给出如下问题:
直线
、
相交于点O,
,
平分
,射线
,求
的度数.
小丽:以下是我的解答过程(部分空缺)
解:如图1,因为射线
,(已知)
所以
______°.(_______________________)
因为
与
互补,
,(已知)
所以
______=______°.(_______________________)
因为
平分
,(已知)
所以
______°.(_______________________)
因为
是直线
下方的一条射线,
所以
______°.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/51b9bdcb-fd8b-492b-933d-ffe460ceec07.png?resizew=288)
(1)请补全小丽的解答过程;
(2)小聪说:“小丽的解答并不完整,符合题意的图形还有一种情况.”请在图2中画出小聪说的另一种情况,并解答.
直线
![](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/ebfcc6ea3a5df3a1c0104f36b3c51455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e7b8a59f8d66176463f3d71f882a26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ebef5bab02280cdc99cc7f689135cd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b2557547eecdc826b8282058802d217.png)
小丽:以下是我的解答过程(部分空缺)
解:如图1,因为射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ebef5bab02280cdc99cc7f689135cd4.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128838eb6cc0c80fbef3c8cdc3c5b8d2.png)
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fed1f57a835af4e9022e27603d12d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e7b8a59f8d66176463f3d71f882a26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebfcc6ea3a5df3a1c0104f36b3c51455.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/785f8669cfca33a75643f6acd31f96b2.png)
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e7b8a59f8d66176463f3d71f882a26.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0008a2088cba73f0c674251a958d28c.png)
因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71398cc39ccfe112c39fcbf5d2c34919.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/51b9bdcb-fd8b-492b-933d-ffe460ceec07.png?resizew=288)
(1)请补全小丽的解答过程;
(2)小聪说:“小丽的解答并不完整,符合题意的图形还有一种情况.”请在图2中画出小聪说的另一种情况,并解答.
您最近一年使用:0次
名校
7 . 如图,直线
与
相交于点O,
平分
,
平分
.
的补角是 ;
(2)若
,求
;
(3)判断射线
与射线
有什么位置关系,并说明理由.
![](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/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc9f91270ddbe1cf3c1362e1b95aee14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22df2977de56cc69be0c1e847653d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/418ebb89d29f4f631b055c911e8d178a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3c80bc57b9ca14e7b943e3ac1afd68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbee6d5731d6f4bb1e4f2ba3d89b7dc.png)
(3)判断射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
您最近一年使用:0次
2024-03-12更新
|
351次组卷
|
6卷引用:山东省德州市宁宁津县大曹镇大赵中学2023-2024学年七年级下学期3月份月考检测数学试题
山东省德州市宁宁津县大曹镇大赵中学2023-2024学年七年级下学期3月份月考检测数学试题(已下线)专题01 相交线与平行线(十一大题型)-【好题汇编】备战2023-2024学年七年级数学下学期期中真题分类汇编(山东专用)山东省德州市乐陵市张桥中学2023-2024学年七年级下学期第一次月考数学试题(已下线)专题01 相交线与平行线之九大题型-备战2023-2024学年七年级数学下学期期末真题分类汇编(人教版)(已下线)七年级数学期末模拟卷(辽宁专用,北师大版全册)-学易金卷:2023-2024学年初中下学期期末模拟考试江苏省无锡市梁溪区江南中学2022-2023学年七年级上学期期末数学试题
2024九年级下·全国·专题练习
8 . 如图是某型号机器人示意图,
是垂直于工作台的移动基座,
,
为机械臂,
,
,
,
,机械臂端点C到工作台的距离![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/8/64e61372-4498-40d7-8f05-bd8daf099beb.png?resizew=299)
(1)
的补角度数是 °;
(2)点A到直线
的距离约是 m;
(3)
的长约是
.(结果精确到
)(参考数据:
,
,
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e92f68167dffe85245938ce7913324b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a375d37c879fbe6732daf4b83e37c867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c253d7e006bf012297c22dc3fa3262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f34269920d413f3a36871d5fccca08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a21f01d497f4a8cd1b3a60e6caaeac5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/8/64e61372-4498-40d7-8f05-bd8daf099beb.png?resizew=299)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
(2)点A到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfaa19eeaf415ed419e77fe92794f443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669574366f342aac23f8fc51d67a80dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669574366f342aac23f8fc51d67a80dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61689fb5150b5ac0aba8b98b888c86e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4abc6249bd34b0c6bc7168993734bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d92accf6e50007ee4b73b16487f78a.png)
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9 . 如图,将长方形纸片
按照如图所示的方式折叠,
为折痕,点B的对应点
在线段
上,若
,则
的度数为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/1df3a071-a5bb-43c9-a7f3-f5b217a9736e.png?resizew=133)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f53caeff4df83df81d132bfb21c2599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968b886a9f161fdcab1e08cba8ece5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b38ab4ca92eaae40c99d8255583ab63d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c95fa8e0d0b64aeff4544404233cba.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/1df3a071-a5bb-43c9-a7f3-f5b217a9736e.png?resizew=133)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 已知:
,则
的补角是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b076bb45db540ffb53af06e6b9676dbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780d8fd6c6c1deeeb45e15f639719e02.png)
您最近一年使用:0次