1 . (1)计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e519eaa08fafe0f5f188eeb77cc6e2.png)
(2)如图,已知
,
,
.试说明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e519eaa08fafe0f5f188eeb77cc6e2.png)
(2)如图,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be554bd401abb0d19c0d9c91a16cdd27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e53497af8899cb299d762f1a4f46a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d384390f4e0a1e0abd4cc19382d94db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b126531871d98f7a5cbdb4efefc161.png)
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2 . 小丽与爸妈在公园里荡秋千,如图,小丽坐在秋千的起始位置
处,
与地面垂直,两脚在地面上用力一蹬,妈妈在距地面
的
处接住她后用力一推,爸爸在
处接住她,
于点
,
于点
,若爸爸到
的水平距离
,
,
(参考数据:
,
,
).
;
(2)求妈妈到
的水平距离(即
的长);
(3)求秋千的起始位置
距地面的高
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01f8039a874d818f0067ad4dc93bdd33.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/5a67bb733403810fa80c0d758e537645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dec44a1f53ea3b2f972012ec84ce0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472a09e99cdd352e69d455723b19260d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/886c25cbaff27a9c4cf52dacec0eac4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b1ab28a1e8e4851895938456ea8e51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f986badfc5dea707c164e2ab6c98dd06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb8485466d2127bd681a322f87c58f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67802092c4c9f3b1cff1f9502b7d1ded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b443674e3ba8c5adc2ce50055b18521.png)
(2)求妈妈到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(3)求秋千的起始位置
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
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3 . (1)计算:
.
(2)如图,在菱形
中,过点
分别作
于点
,
于点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c580b67566fdf64530d902f58af7425.png)
(2)如图,在菱形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c38dfd14dde969702dff97ef2270f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d276d0010fd458383ea3dd61415e1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7faabc484ce3666706c1beffda4bcfe2.png)
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4 . 如图所示,在四边形
中,
,点F是
的中点,连接
并延长交
的延长线于点E.
的面积与
的面积相等;
(2)若
平分
,试猜想线段
、
、
之间的数量关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff575e55857af133edb24c8e61504f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2947ca8e0cdbeb4aab80ce9e7b63ba98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
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名校
5 . 在直角坐标系中,点
绕原点O逆时针旋转
,得到的点的坐标是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41c0317631fd145d5c5f1e85ed8841d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-05-06更新
|
42次组卷
|
2卷引用:江西省吉安市2023-2024学年八年级下学期期中数学试题
名校
6 . 课本再现:在一个角的内部,到角的两边距离相等的点在这个角的平分线上.
,易知:
平分
.
知识应用:
(1)如图2,
,求证:
平分
.
(2)如图3,四边形
中,
,则
______(用含
的代数式表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09048b1687b7f180ff0ad748c7a5045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
知识应用:
(1)如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d506f8ee021db53a18c7aaa76d06febb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
(2)如图3,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d018706593e44c0b01e05eef2424969.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/349ba672373d29a175c9e96eb9121606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-04-19更新
|
85次组卷
|
3卷引用:江西省吉安市永新县十校联考2023-2024学年八年级下学期第一次月考数学试题
7 . 课本再现:
承前启后:
前面已经证明了“等腰三角形的两底角相等”;反过来,命题“有两个角相等的三角形是等腰三角形”成立吗?事实上,可以发现并证明上述命题是等腰三角形的一个判定定理.
定理证明:
(1)小敏根据上述定理,已经写出了已知,求证,请你完成证明过程.
已知:如图1,在
中,
,求证:
.
解决问题:
(2)如图2,一架飞机在距离地面
的高空上自东向西飞行,飞机在
处测得地面某小岛
在其南偏西
方向,飞行一段距离后,在
处测得小岛
在其南偏西
方向,求
之间的距离.
承前启后:
前面已经证明了“等腰三角形的两底角相等”;反过来,命题“有两个角相等的三角形是等腰三角形”成立吗?事实上,可以发现并证明上述命题是等腰三角形的一个判定定理.
定理证明:
(1)小敏根据上述定理,已经写出了已知,求证,请你完成证明过程.
已知:如图1,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4354365ca0929f8a606ed0bf341e4ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/29/fc5b3e58-0dbc-48f2-a1c4-521c40fe1db9.png?resizew=82)
解决问题:
(2)如图2,一架飞机在距离地面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a1726d9f6503e1399ce780776108eb1.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/be6a6301878fed2a01413020b27310a5.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/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/29/3ee5faad-3ed3-4eb4-a1fd-609fc33d39c0.png?resizew=186)
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2024-04-01更新
|
43次组卷
|
2卷引用:江西省吉安县文博学校2023-2024学年八年级下学期月考数学试题
8 . 如图,点E,F分别在正方形
的边
上,
,点M是
的中点,过点M的直线与正方形的一组对边交于点P,Q(与点E,F不重合),点P在
或
上.若
则
的长为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11944f055fd806016ae3576019d4bf30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a691c39f61299017e598a347d7b33d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f1aaa266658c3dd8ccce3b705672f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
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2024-03-31更新
|
19次组卷
|
4卷引用:江西省吉安市吉安县2023-2024学年九年级下学期月考数学试题
江西省吉安市吉安县2023-2024学年九年级下学期月考数学试题江西省九江市第十一中学2023-2024学年九年级上学期期末数学试题(已下线)专题04 矩形、菱形、正方形性质与判定期末真题汇编【八大题型+优选提升题】-备战2023-2024学年八年级数学下学期期末真题分类汇编(人教版)(已下线)八年级数学期末模拟卷(湖南省专用,湘教版全册)-学易金卷:2023-2024学年初中下学期期末模拟考试
9 . 如图,给出下列论断:①
,②
,③
.请你从中任选两个 作为条件,另一个作为结论构成一个命题(写一种情况即可),并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0487ebca22d4aa1233073f81fd70a424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e53497af8899cb299d762f1a4f46a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0bd8869f34219e7fbe5a9b8842667c1.png)
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2024-03-28更新
|
47次组卷
|
2卷引用:江西省吉安县文博学校2023-2024学年八年级下学期月考数学试题
10 . 通过对下面数学模型的研究学习,解决下列问题:.
【模型呈现】
某兴趣小组在从汉代数学家赵爽的弦图(如图1,由外到内含三个正方形)中提炼出两个三角形全等模型图(如图2),即“一线三等角”模型和“K字”模型.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/71abb32e-e97e-4030-a90f-8f2e4e883c63.png?resizew=601)
(1)请在上图2中选择其中一个模型进行证明
.
【模型应用】
(2)如图3,正方形
中,
,
,求
的面积.
(3)如图4,四边形
中,
,
,
,
,
,求
的面积.
【模型呈现】
某兴趣小组在从汉代数学家赵爽的弦图(如图1,由外到内含三个正方形)中提炼出两个三角形全等模型图(如图2),即“一线三等角”模型和“K字”模型.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/71abb32e-e97e-4030-a90f-8f2e4e883c63.png?resizew=601)
(1)请在上图2中选择其中一个模型进行证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a391c4d96cfb4e7c0f1df58a94be7218.png)
【模型应用】
(2)如图3,正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5427b7b994b860628df3d6b7a07de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a19338598965bb3856cdd0236bbf694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
(3)如图4,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dceb5cc71fc50f20649f6b9535fd914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea0de02043149fdb574b7c820ac7df1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a32884afd5c49777628d70827a9d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3620030e8808da46df97330103827913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/5a48e971-3dd9-4e80-9b3f-d78f1805b6ce.png?resizew=299)
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