1 . 如图,已知
是线段
上的一点,
是线段
的中点,
是线段
的中点,
为
的中点,
是
的中点,则
等于______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccfff99dd307eb936b5e5263e43ca510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1165830b314a0dab65ea267e82bd3f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c493e1a59ab74a246219bb54dbf3f0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/9a7c5436-60a7-41ce-8961-59cf7824b046.png?resizew=224)
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2 . 如图,两半圆的圆心点
分别在直角
的两直角边
上,直径分别为
,如果两半圆相外切,且
,那么图中阴影部分的面积为( ).
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/6/8be63afe-f846-43ac-a5fc-056ed3a05358.png?resizew=158)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2873768ae11fc212fc1fbd9edbc85f26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d54431bbb28ebd98db5c1dc6083a75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28d2790a97390935125aa897417f970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c72b972f847fc98a41077917cc9077.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/6/8be63afe-f846-43ac-a5fc-056ed3a05358.png?resizew=158)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 在矩形
中,
,对角线
相交于点
,点
是对角线
上关于点
对称的两点,点
关于
的对称点分别为点
,点
关于
的对称点分别为点
,若由点
构成的四边形为菱形,则
的长度为______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa5be4533c99ad35b58bbe504c06a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d578394cd8e4d7a705599269c512960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdb2c8786b3375fa19b35cd9343a9b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a20cb2c77ea29b6eabbc477bc3743859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83fd42df335c85bf92b7961b9851977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab0ed07775b0fdcb368b696a0f65422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
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名校
4 . 乘法公式的探究及应用.
(1)如图,可以求出阴影部分的面积是______(写成两数平方差的形式);
(2)如图,若将阴影部分裁剪下来,重新拼成一个长方形,它的宽是______,长是______,面积是______(写成多项式乘法的形式);
(3)比较左、右两图的阴影部分面积,可以得到乘法公式______.
A.
B.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb5f9bbea615b4280e7e6e4af71afc3.png)
C.
D.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/c3998b2b-4f50-4602-b7a5-370dbbb7346a.png?resizew=291)
(1)如图,可以求出阴影部分的面积是______(写成两数平方差的形式);
(2)如图,若将阴影部分裁剪下来,重新拼成一个长方形,它的宽是______,长是______,面积是______(写成多项式乘法的形式);
(3)比较左、右两图的阴影部分面积,可以得到乘法公式______.
A.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e5c33e6c069b8c55493b6dbccd90f4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb5f9bbea615b4280e7e6e4af71afc3.png)
C.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eec3704e6f7d2d2caddaecb17745b0c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ffa33e6a7fb4c7f0aaf1c9065578704.png)
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名校
5 . 如图,已知
,
平分
,且
,则
的度数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0cf7633fe1cf4a393c17d56d8683dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc96919f50801279ee2e368e5c80a376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fed1f57a835af4e9022e27603d12d31.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/e6b405f7-20fb-4e8b-bffa-63734ac36dbd.png?resizew=172)
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6 . 在数学活动课上,老师和同学们开展了以“线段与角的共性”为主题的数学活动.研究发现线段中点的概念与角平分线的概念类似,甚至它们在计算方法上也有类似之处,它们之间的题目可以互相转化,解法可以互相借鉴.如图1,点
是线段
上的一点,
是
的中点,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/e0c0fa2d-148e-4d8c-8f13-97047f76b020.png?resizew=497)
(1)会用数学的眼光观察:
①若
,
,则
的长度为______;
②若
,
,则
的长度为______;
(2)会用数学的语言表达:“创新”小组的同学类比想到:如图2,已知
,在角的内部作射线
,再分别作
,
的角平分线
,
.
③若
,则
的度数为______;
④若
,则
的度数为______;
(3)会用数学的思维分析:“慎密”小组在“创新”小组的基础上提出:如图3,若
,在角的外部作射线
,再分别作
,
的角平分线
,
.若
,则
的度数为______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/e0c0fa2d-148e-4d8c-8f13-97047f76b020.png?resizew=497)
(1)会用数学的眼光观察:
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d42e97eee705d164e6ac6de9ecd6d1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df81cda12d7601d58b1d9c7c180c4d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(2)会用数学的语言表达:“创新”小组的同学类比想到:如图2,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6978615637bd3febf56d23798f65306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fed1f57a835af4e9022e27603d12d31.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)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72dbe710cca6662be5cc0c26a0d12a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27935c1ef4df2d52ac697678a3c8f39d.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e928b8e0318a841cd9fb53636820e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27935c1ef4df2d52ac697678a3c8f39d.png)
(3)会用数学的思维分析:“慎密”小组在“创新”小组的基础上提出:如图3,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff73892a5566e1eff4955174277e24d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fed1f57a835af4e9022e27603d12d31.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/4e928b8e0318a841cd9fb53636820e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27935c1ef4df2d52ac697678a3c8f39d.png)
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7 . 如图,已知反比例函数
的图象经过面积为8的矩形
的顶点A,则k的值为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf319e356d95444e3704cc551d62364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ca6d348c4c0f53eb995246e1cb5ae7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/f14ed01a-0cd0-4937-aae3-22c40b6b19fa.png?resizew=100)
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8 . 某同学在某层教学楼上测得楼前一棵树
的顶端点A的俯角为
,如果这名同学所站的位置点C的高度为24米,且点C到直线
的距离为10米,那么这棵树的高度
为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.9米 | B.![]() | C.![]() | D.![]() |
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名校
9 . 如图所示,
,
,那么小于
的角有______ 个,它们的度数之和是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1309fbd835cf1a8b913d19f57b2b374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddcb352768a5f5e931f0e624bdb50052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/176a4e98-f1f8-4955-a947-35d3ee01819b.png?resizew=117)
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10 . 尺规作图题:如图,已知线段
、
,按以下要求画线段(不写作法,保留作图痕迹)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/6/b6ff7ebb-c360-4e2f-be51-3bf8f80bdbd7.png?resizew=126)
(1)作
.
(2)作
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/6/b6ff7ebb-c360-4e2f-be51-3bf8f80bdbd7.png?resizew=126)
(1)作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93a120e7d05950c06e9e6737c36b4b8e.png)
(2)作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/269629f00433d711e58682463a3891a2.png)
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