名校
1 . 定义:如图(1),若分别以
的三边
,
,
为边向三角形外侧作正方形
,
和
,则称这三个正方形为
的外展三叶正方形,其中任意两个正方形为
的外展双叶正方形.
(1)作
的外展双叶正方形
和
,记
,
的面积分别为
和
;
①如图(2),当
时,求证:
;
②如图(3),当
时,
与
是否仍然相等,请说明理由.
(2)已知
中,
,
,作其外展三叶正方形,记
,
,
的面积和S,请利用图(1)探究:当
的度数发生变化时,
的值是否发生变化?若不变,求出
的值;若变化,求出
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60c3b75ff1610956dfe9a9cd7692d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02b1139e07e431b5d4276757b232bad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/5/a2011946-b318-42a8-b754-447c2181faca.png?resizew=550)
(1)作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60c3b75ff1610956dfe9a9cd7692d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13668f033d00acfc366f7e47949c4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
①如图(2),当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31dd78e9156dcf6db93f6cbcc5b43b14.png)
②如图(3),当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d32993a87a53ae4aab52e8c717aa68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13668f033d00acfc366f7e47949c4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654a3aacb8539b4996023caf5b55c85e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a690101e5595786c62946c4b29b665f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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2023-08-23更新
|
285次组卷
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6卷引用:2016-2017学年重庆市江津实验中学、李市中学、白沙中学八年级下学期期中联考数学试卷
名校
2 . 如图,在
中,
平分
交
于点
,点
,
分别是
和
上的动点,当
,
时,
的最小值等于_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4066ed8dde07a00665ad52a5d15c7531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4494a85de0be0b97a69348115aef8513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95e98288acdd662de9a3dae1fcf0368.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/13/f489c08d-11e6-455f-9187-c26d867b2e5b.png?resizew=108)
您最近一年使用:0次
2023-06-08更新
|
503次组卷
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13卷引用:江苏省南通市八一中学2019-2020学年八年级上学期10月月考数学试题
江苏省南通市八一中学2019-2020学年八年级上学期10月月考数学试题江苏省南通市启秀中学2019-2020学年八年级上学期9月月考数学试题江苏省南京市树人学校2020-2021学年八年级上学期10月月考数学试题江西省宜春市丰城中学2022-2023学年七年级下学期期末数学试题江苏省泰州市第二中学附属初中2021-2022学年八年级上学期第一次月考数学试题江苏省徐州市鼓楼区徐州树德中学2021-2022学年八年级上学期10月月考数学试题福建省厦门市大同中学2022-2023学年八年级上学期期中数学试卷江苏省常州市钟楼区花园中学2022-2023学年八年级上学期10月月考数学试题陕西省渭南市白水县2021-2022学年八年级上学期期末考试数学试卷河南省方城县六校联考2022-2023学年八年级上学期第二次月考数学试题广东省佛山市禅城区第十四中学2022-2023学年七年级下学期期中数学试题江苏省泰州市姜堰区2023-2024学年八年级上学期10月月考数学试题陕西省安康市汉阴县2023-2024学年八年级上学期期末数学试题
名校
3 . 如图,在△ABC中.AB=AC,点E在线段BC上,连接AE并延长到G,使得EG=AE,过点G作GD∥BA分别交BC,AC于点F,D.
(1)求证:△ABE≌△GFE;
(2)若GD=3,CD=1,求AB的长度;
(3)过点D作DH⊥BC于H,P是直线DH上的一个动点,连接AF,AP,FP,若∠C=45°,在(2)的条件下,求△AFP周长的最小值.
(1)求证:△ABE≌△GFE;
(2)若GD=3,CD=1,求AB的长度;
(3)过点D作DH⊥BC于H,P是直线DH上的一个动点,连接AF,AP,FP,若∠C=45°,在(2)的条件下,求△AFP周长的最小值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/e01919cf-db35-4555-8625-ce3b9885d116.png?resizew=327)
您最近一年使用:0次
2020-11-20更新
|
755次组卷
|
2卷引用:湖南省长沙市天心区长郡教育集团2020-2021学年八年级上学期期中数学试题
4 . 如图1,若分别以△ABC的AC、BC两边为边向外侧作的四边形ACDE和BCFG为正方形,则称这两个正方形为外展双叶正方形.
(1)发现:如图2,当∠C=90°时,求证:△ABC与△DCF的面积相等.
(2)引申:如果∠C
90°时,(1)中结论还成立吗?若成立,请结合图1给出证明;若不成立,请说明理由;
(3)运用:如图3,分别以△ABC的三边为边向外侧作的四边形ACDE、BCFG和ABMN为正方形,则称这三个正方形为外展三叶正方形.已知△ABC中,AC=3,BC=4.当∠C=_____°时,图中阴影部分的面积和有最大值是________.
(1)发现:如图2,当∠C=90°时,求证:△ABC与△DCF的面积相等.
(2)引申:如果∠C
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411837b4b3078d05b43cb0439259a362.png)
(3)运用:如图3,分别以△ABC的三边为边向外侧作的四边形ACDE、BCFG和ABMN为正方形,则称这三个正方形为外展三叶正方形.已知△ABC中,AC=3,BC=4.当∠C=_____°时,图中阴影部分的面积和有最大值是________.
![](https://img.xkw.com/dksih/QBM/2017/6/15/1709539610451968/1710773279678464/STEM/0668f07494534095ac3058233b8e1ab4.png?resizew=515)
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2016-12-05更新
|
1799次组卷
|
6卷引用:江西省吉安市樟山中学2017届九年级中考最后一模数学试题
名校
5 . 在菱形
中,
,点
是对角线
上一动点,将线段
绕点
顺时针旋转
到
,连接
.
![](https://img.xkw.com/dksih/QBM/2020/3/12/2417889064411136/2418067895074816/STEM/6fe16ceb9ce54b2cab7dfa991e1db78d.png?resizew=397)
(1)如图1,求证:
;
(2)如图2,连接
并延长,分别交
、
于点
、
.
①求证:
;②若
的最小值为
,直接写出菱形
的面积为 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53330c107f8245290a5a42c3d356acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3525ddc5153fada64eaf14e50b536542.png)
![](https://img.xkw.com/dksih/QBM/2020/3/12/2417889064411136/2418067895074816/STEM/6fe16ceb9ce54b2cab7dfa991e1db78d.png?resizew=397)
(1)如图1,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7de647545408c70dda9f7063baedf35.png)
(2)如图2,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f6927cc2a930203ac34366383e76ef.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa60af8a0b0a4c748e50f8b677677183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2020-03-12更新
|
259次组卷
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2卷引用:2020年湖北省武汉市元月调考数学一模试题