在矩形ABCD中,∠AOB=60°,AB=4
,求BC的长.
![](https://img.xkw.com/dksih/QBM/2013/2/26/1573605303074816/1573605353914368/STEM/086109a439114b6297b21215aa5c0ba0.png)
![](https://img.xkw.com/dksih/QBM/2013/2/26/1573605303074816/1573605353914368/STEM/f9f8c219d144463581d979f5366d308c.png)
更新时间:2016-12-05 16:11:11
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解答题-证明题
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【推荐1】如图,在
中,
,
是BC的中点,
于点E,
于点F.
(1)若
,求证:
是等边三角形;
(2)如果
,
,求DE的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.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/761a77e11e1e45c2a8b2d34d22cf8e04.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0b4de7037d1917b0a964db6438df07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914a0f9a14fd49a938a90618cc5843e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f186ea827f7becafd1ac4955e22c6812.png)
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解答题-证明题
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【推荐2】如图,
为
的直径,弦
于点E,连接
并延长交
于点F,连接
,
.
![](https://img.xkw.com/dksih/QBM/2022/11/3/3101543930396672/3101801585262592/STEM/5d84c70e0f9c4c8da9a4c27276123a24.png?resizew=143)
(1)求证:
;
(2)连接
,若
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b63d2504bd3ecce8c10560b142356f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4d997e2f22397b870401ccc397a5a9.png)
![](https://img.xkw.com/dksih/QBM/2022/11/3/3101543930396672/3101801585262592/STEM/5d84c70e0f9c4c8da9a4c27276123a24.png?resizew=143)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b1228ebf9a05c67644357de374bb2f2.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b65065ec3a0cb4b050989165c003d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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解答题-问答题
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【推荐1】如图,在平面直角坐标系中,O为坐标原点,直线
交x轴的负半轴于点A,交y轴的正半轴于点B,
,点C在x轴的正半轴上,
,点D在第四象限的直线
上,
于点E,
.
![](https://img.xkw.com/dksih/QBM/2022/10/24/3094765868859392/3096762494935040/STEM/f8933e980ec0472596ee12ce8fb393ce.png?resizew=114)
(1)求直线
的解析式;
(2)求点D的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07565f10847840e0fb07b05218ad17fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c406e7d1e7977dd5b30ef81cfdc8e8d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eacc72119139a8d891ba5b7de6c7332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c38dfd14dde969702dff97ef2270f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6697ff2e6731c7bc666ce7a384daef3b.png)
![](https://img.xkw.com/dksih/QBM/2022/10/24/3094765868859392/3096762494935040/STEM/f8933e980ec0472596ee12ce8fb393ce.png?resizew=114)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)求点D的坐标.
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解答题-作图题
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【推荐2】已知在
中,
.
(1)请用尺线作图画出线段
的垂直平分线交
于点
,交
于点
;
(2)在(1)的条件下,连接
,若
,
时,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/16/c530b87d-876b-451f-84ac-fa9655c5fefd.png?resizew=160)
(1)请用尺线作图画出线段
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)在(1)的条件下,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0763b031b7e6b6d87ce3554ac482d5.png)
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解答题-证明题
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【推荐1】把宽与长之比为
的矩形叫做黄金矩形,黄金矩形令人赏心悦目,它给我们以协调、匀称的美感,如图,四边形
是黄金矩形,如果在这个黄金矩形里画一个正方形,那么剩下的矩形(矩形:
)还是黄金矩形吗?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0b653216cbc4d46f5f0b43ab18ed94.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/30/01561c76-be34-4ae2-a3bb-ac18455f1d9b.png?resizew=154)
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解答题-证明题
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【推荐2】四边形ABCD为正方形,点E为线段AC上一点,连接DE,过点E作EF⊥DE,交射线BC于点F,以DE、EF为邻边作矩形DEFG,连接CG.
![](https://img.xkw.com/dksih/QBM/2020/9/8/2545438666416128/2546304545144832/STEM/ce2237d5da904f91bb608789f0f80a41.png?resizew=312)
(1)如图,求证:矩形DEFG是正方形;
(2)当线段DE与正方形ABCD的某条边的夹角是35°时,求∠EFC的度数.
![](https://img.xkw.com/dksih/QBM/2020/9/8/2545438666416128/2546304545144832/STEM/ce2237d5da904f91bb608789f0f80a41.png?resizew=312)
(1)如图,求证:矩形DEFG是正方形;
(2)当线段DE与正方形ABCD的某条边的夹角是35°时,求∠EFC的度数.
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