名校
1 . 如图,已知四棱锥
的底面是菱形,对角线
交于点
,
,
,
底面
,
分别为侧棱
的中点,点
在
上且
.
四点共面;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e3dfcd8aff269dd5aba398816490c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ba1df94176a1f769c7a0a12bf357fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4e6e2c17ac95483a840da8ddc85be9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930e85bc9f73e86cfb6ce9b076433f1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed30b73beeccafd4ec854237b33e1e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccfe1ad40befb43ffa3033dac111e12f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
您最近一年使用:0次
2024-06-04更新
|
975次组卷
|
2卷引用:湖南省长沙市第一中学2024届高三下学期模拟考试数学试卷(一)
名校
解题方法
2 . 如图,在以A,B,C,D,E,F为顶点的六面体中(其中
平面EDC),四边形ABCD是正方形,
平面ABCD,
,且平面
平面
.
为棱
的中点,证明:
四点共面;
(2)若
,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/001e90e232a254b9a57dc3339ea265dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a38e6c6dfde2b19b6b47f35a439a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5493b819f911918c69ee006b0a4827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02b6df2041ef74bd8a80c9f1ab7cf47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466fabcaac59132fea648ff35342ec9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e74186ac772d27f6427b284e25bfa7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad998188c33f18f04ba8891f700b466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/112a1a3346aa0acbe5f59ffe0a319912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62871bb0dff211fc3bd80f9066c25b29.png)
您最近一年使用:0次
2023-01-10更新
|
3601次组卷
|
13卷引用:湖南省长沙市2023届高三上学期新高考适应性考试数学试题
湖南省长沙市2023届高三上学期新高考适应性考试数学试题湖南省岳阳市平江县第一中学2023届高三下学期适应性考试(二)数学试题湖南省岳阳市华容县2023届高三上学期普通高中新高考适应性考试数学试题浙江省宁波市镇海中学2023届高三下学期4月统一测试数学试题湖南省长沙市长郡湘府中学2023-2024学年高三上学期入学考试(暑假作业检测)数学试题(已下线)2024届数学新高考Ⅰ卷精准模拟(八)浙江省名校协作体2022-2023学年高二下学期开学联考适应性考试数学试题广东省珠海市第一中学2023届高三下学期2月阶段性考试数学试题专题16空间向量与立体几何(解答题)重庆市第一中学校2022-2023学年高一下学期4月月考数学试题福建省福州第八中学2024届高三上学期期中考试数学试题江苏省无锡市第六高级中学2024届高三上学期12月教学质量调研数学试题(已下线)【一题多变】四点共面 向量转化
解题方法
3 . 如图①,在直角梯形ABCD中,
,四边形ABEF是正方形:现将正方形ABEF沿AB折起到四边形
的位置,使平面
平面ABCD,M为
的中点,如图②.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712444928262144/2713253561049088/STEM/d5b59f79-8aef-496c-b936-56e88c0b1ff1.png?resizew=515)
(1)证明:直线DC与直线
相交;
(2)求直线BM与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2982ce1ba17b09019f2ada05537f83a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86a641aef4e86274984172782b0e486b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17c9e307f559ff7e27c8fbc7e49be1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712444928262144/2713253561049088/STEM/d5b59f79-8aef-496c-b936-56e88c0b1ff1.png?resizew=515)
(1)证明:直线DC与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dc0af163c13e7fed944bf0648df7c89.png)
(2)求直线BM与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9761893b0cc4aee26decca8869bf870.png)
您最近一年使用:0次
解题方法
4 . 如图,直四棱柱
中,四边形
为梯形,
,且
.过
三点的平面记为
,
与
的交点为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/1/38e8f68b-6006-41bd-9470-b1a0cf9265eb.png?resizew=142)
(1)证明:
为
的中点;
(2)求此四棱柱被平面
所分成上下两部分的体积之比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](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/e839ac941e8bf536ff35a12e56c7a400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0dfa9d9e982eafd09e850cfdaeea2a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/1/38e8f68b-6006-41bd-9470-b1a0cf9265eb.png?resizew=142)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
(2)求此四棱柱被平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
2017-10-10更新
|
625次组卷
|
2卷引用:2020届湖南省邵阳市重点学校高三下学期综合模拟考试数学(文)试题