1 . 如图,在
中,
于点
.分别以
为边向外作正方形,得到较大的三个正方形的面积分别为
,那么最小的正方形面积为()
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/b8446390-08b5-4d1e-bcea-40ce1112cdb9.png?resizew=202)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5632257c8a02f4cd0989df545fdaa41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/148ebc1e587c6afc551bad2a7f2d44fb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/b8446390-08b5-4d1e-bcea-40ce1112cdb9.png?resizew=202)
A.5 | B.6 | C.7 | D.![]() |
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2 . 有一个边长为1的大正方形,经过2次“生长”后,在它的左右肩上生出两个小正方形,其中,三个正方形围成的三角形是直角三角形,再经过1次“生长”后,形成的图形如图所示,如果继续“生长”下去,它将变得“枝繁叶茂”,那么“生长”了2023次后形成的图形中所有的正方形的面积和是( )
A.2024 | B.2023 | C.![]() | D.![]() |
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2024-02-28更新
|
206次组卷
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2卷引用:贵州省遵义市2022-2023学年八年级下学期期中数学试题
3 . 勾股定理是人类最伟大的科学发现之一.如图1,以直角三角形
的各边为边分别向外作正方形,再把较小的两张正方形纸片按图2的方式放置在最大的正方形内,三个阴影部分面积分别记为
,
,
,若已知
,
,
,则两个较小正方形纸片的重叠部分(四边形
)的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a41ee1f8d4b35e625e3421d2800cf3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0863cf59114f905e9ad3debc5572792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c705ed1d40eb3d40ebadd05dbb645b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2257da1e2425f2ea9ac7440f52659ff.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/ce108b69-a83e-443b-a5ee-0c2fcc8afebe.png?resizew=247)
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4 . 在我国汉代数学家赵爽为了证明勾股定理,创制了一幅“弦图”(如图1),后人称之为“赵爽弦图”,流传至今.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/90a86d0b-da97-4a5b-bf9e-14e4508c7636.png?resizew=517)
(1)勾股定理的证明,人们已经找到了400多种方法,请从图1,图2,图3的证明方法中任选一种来证明该定理.
(2)如图4所示,分别以直角三角形三边为直径作半圆,设图中两个月形图案(图中阴影部分)的面积分别为
,
,直角三角形面积为
,请判断
,
,
的关系并证明.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/90a86d0b-da97-4a5b-bf9e-14e4508c7636.png?resizew=517)
(1)勾股定理的证明,人们已经找到了400多种方法,请从图1,图2,图3的证明方法中任选一种来证明该定理.
(2)如图4所示,分别以直角三角形三边为直径作半圆,设图中两个月形图案(图中阴影部分)的面积分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
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5 . 如图,
,
,分别以各边为直径作半圆,图中阴影部分在数学史上称为“希波克拉底月牙”,当
,
时,则阴影部分的面积为____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae8221601c7bd5c51fd520615581fa1.png)
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2卷引用:广东省梅州市五华县2023-2024学年八年级上学期期末数学试题
6 . 如图,分别以直角三角形的三边为直径的三个半圆的面积从小到大依次为
,则
之间的关系正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/32b4eeb2-3f77-40b2-9de3-447c1579691a.png?resizew=152)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f62d3ef6de35b31fcf8efe2aaa72070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f62d3ef6de35b31fcf8efe2aaa72070.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/32b4eeb2-3f77-40b2-9de3-447c1579691a.png?resizew=152)
A.![]() ![]() | B.![]() |
C.![]() | D.![]() |
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7 . 数学家欧几里得利用如图验证了勾股定理.以
的三条边为边长向外作正方形
,正方形
,正方形
,连接
.若
,则
的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c35e7a990d8ff3e55945fd4718a9740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/616b46476c1f1d22e3a21d6fa33a3400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/324496bd9872abd0867bed2f5aca4a43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
A.40 | B.32 | C.24 | D.18 |
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4卷引用:福建省福州第十九中学2023-2024学年八年级上学期期末数学试题
福建省福州第十九中学2023-2024学年八年级上学期期末数学试题福建省福州十九中、延安中学2023-2024学年八年级上学期期末数学试题(已下线)第18章 平行四边形(单元测试·基础卷)-2023-2024学年八年级数学下册基础知识专项突破讲与练(人教版)安徽省阜阳市第一初级中学2023-2024学年八年级下学期期中数学试题
8 . 如图,在直角三角形
中,
,以
,
,
为边作正方形
,正方形
,正方形
.设
的面积为
,
的面积为
,
的面积为
,四边形CHET的面积为
,四边形
的面积为
,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/2/074fde15-ca23-4f9b-8014-24de7a32ce17.png?resizew=187)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/616b46476c1f1d22e3a21d6fa33a3400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2de15162b13ba943f8da2498580cf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d43eb0b274e00cbbc4a210da4165042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e64c953aaf341e772a5fe776fbc78a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530f5b63e797195906285c0c03eb9276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ec4e283ae239efa1bad5dfe0216bd97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c2d5971afbff8eca1b9aff5f76f710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e204eeda3cbe67e9e709be5c790b49f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bea2e33fa471874d1c62700cf80a4ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3549a6c9f727de6be285bcaa281f2f48.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/2/074fde15-ca23-4f9b-8014-24de7a32ce17.png?resizew=187)
A.![]() | B.![]() |
C.![]() | D.![]() |
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9 . 如图,以Rt
的两边
为边向外所作正方形的面积分别是
,则以另一边
为直径向外作半圆的面积为______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90b40c2b0ab8e1cfe5112d428b4b829f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8703d807c710305fb87329de205fc0ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ce13774b09ff2edddaf21a072cf60a.png)
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3卷引用:江苏省南京市建邺区2023-2024学年八年级上学期期末数学试题
10 . 如图所示,在
中,
,
,
,
于点D,求
的长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/53af27a4-e5f9-41d5-81c5-bc65d403b2e8.png?resizew=171)
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