如图,在菱形
中,
交于点O,E为
延长线上的一点,且
,连接
分别交
于点F、G,连接
,求证:①
;②四边形
是菱形;③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da095b73d6a1c16e9a2be2df1090ac29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c746500b08d2340fe4ead18f7a84849d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df34369163e511f14028168cb0b21186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f869bea4fca24915497d6a4179c805af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307bd991211ec79b47a4be52933bb8e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce01efb268fda5e385027936d982807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da095b73d6a1c16e9a2be2df1090ac29.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/1/537ac3f4-0afe-48ce-8086-f395bd820e1f.png?resizew=171)
更新时间:2024-03-01 18:30:00
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【推荐1】如图,在等边三角形ABC的三边上,分别取点D,E,F,使得AD=BE=CF求证:△DEF为等边三角形,.
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【推荐2】如图,
为等边△ABC的外接圆,半径为2,点D在劣弧
上运动(不与点A,B重合),连接DA,DB,DC.求四边形ADBC的面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
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【推荐1】如图,在
中,E,F分别是边
的中点,G是
的中点,连接
并延长,交
的延长线于点D,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/510634e49198fc429d942d00fa5446ab.png)
![](https://img.xkw.com/dksih/QBM/2022/12/1/3121484877856768/3126356780244992/STEM/cae2ea456ae4415a82279650d10bcb72.png?resizew=212)
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【推荐2】已知在
中,点
分别是边
的中点,过点
的直线交
的延长线于点
,连接
.求证:四边形
是平行四边形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a887678ca42faa3d289e2b6460790b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b5faf97cb142c3cbab7d3dcaece581.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83fd42df335c85bf92b7961b9851977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3916335d21944e8da24a05ef10f1540f.png)
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【推荐1】如图,在菱形
中,对角线
与
相交于点O,图中有多少个等腰三角形和直角三角形?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/2021/10/15/2829821761323008/2832242546745344/STEM/fef40b0f-e8ab-4355-937b-b88fe215558f.png?resizew=228)
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【推荐2】如图,点O是菱形ABCD的对角线的交点,
,
,连接OE.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/20/a7894bc5-322f-446e-b9cd-13009333b4f5.png?resizew=157)
(1)求证:四边形OCED是矩形;
(2)如果
,
,连接AE,求线段AE的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105068b25f5a63af32f4082cfe08691e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3275b04cb57af1d26fe2562cc4daa445.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/20/a7894bc5-322f-446e-b9cd-13009333b4f5.png?resizew=157)
(1)求证:四边形OCED是矩形;
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b30a38719bbb13cf0c560fd1f7b921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f72d570ef57a07e6a5643c6831589f29.png)
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【推荐1】在
中,M是斜边
的中点,点D在直线
外,且
,连接
.
;
(2)如图2,E是边
上一点,且
,
,求证:四边形
是菱形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f38105b701adcd96b87f27225ca14e95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a929fca455b19682d2a26ecc302123d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650c6c818df102a83ce5159e3208d01a.png)
(2)如图2,E是边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d837ec3d7e3023efee246ac576970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c0aa4c793921fdaa5d430cb90d78ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521e7030f3b7a78e2167e342cc741543.png)
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【推荐2】如图,在△ABC中,∠ACB=90°,BC的垂直平分线分别交BC、AB于D、E,过C作CF∥AB,交BC的垂直平分线于F,连接BF.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/14/cb693f83-bf5e-466c-82e8-658196828bf6.png?resizew=188)
(1)先判断四边形BECF的形状,再进行证明;
(2)当∠A满足什么条件时,四边形BECF是正方形?证明你的结论.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/14/cb693f83-bf5e-466c-82e8-658196828bf6.png?resizew=188)
(1)先判断四边形BECF的形状,再进行证明;
(2)当∠A满足什么条件时,四边形BECF是正方形?证明你的结论.
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