名校
解题方法
1 . 如图,在正方体
中,
,点
在正方体内部及表面上运动,下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/c95a977b-c7bb-4d9c-b84a-bac4448a2d43.png?resizew=158)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/c95a977b-c7bb-4d9c-b84a-bac4448a2d43.png?resizew=158)
A.若![]() ![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
2 . 如图,在多面体
中,平面
平面
,
平面
和
均为正三角形,
为线段
的中点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
面
;
(2)求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17580410bf63dba4fe164265afaac4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3cfd6b6a7e911d10d1a4bed9ca5e749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46a5ce5c10b7a419055abf43764fce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176385d91d5e29324fce4a932eff6a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9926397d0839f1a02946828dc348a7d.png)
您最近一年使用:0次
2023-11-30更新
|
229次组卷
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3卷引用:重庆市永川北山中学校2023-2024学年高二上学期期中考试数学试题
重庆市永川北山中学校2023-2024学年高二上学期期中考试数学试题四川省泸州市泸县第五中学2023-2024学年高二上学期期末数学试题(已下线)湖南省长沙市四县区2024届高三下学期3月调研考试数学试题变式题11-15
名校
3 . 在三棱台
中,
平面
,
,
,
分别为
,
的中点.
(1)证明:
∥平面
.
(2)若
,在线段
上是否存在一点
,使得
与平面
所成角的正弦值为
?若存在,求
的长度;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9ad711b25c36dae0c2a2cedff9954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549b72a555d1cd42e5565a2097b5958f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/28/41210dc4-ccb1-471b-bc22-0656b625dc7b.png?resizew=160)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5a463a03c549b0dba6d90e7f16a2af.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4fcf607b0710d12aaabd17fd053d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/456175ea34492f0bc025aaab668fa659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d172f55bc57ef5b5c2c1ad5b167440b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
您最近一年使用:0次
2023-10-11更新
|
440次组卷
|
4卷引用:重庆市永川萱花中学校2023-2024学年高三上学期期中考试数学试题
名校
解题方法
4 . 如图,矩形
和梯形
,
,
,平面
平面
,且
,
,过
的平面交平面
于
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/3b76558d-a962-4c56-95ba-e85d81c720d3.png?resizew=116)
(1)求证:
;
(2)当
为
中点时,求点
到平面
的距离;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ad6f8846d4294ae3789a6ddd17af5b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/058f36d315245b63a811d5c6f348c17b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c674dc5024374f53920947c4cf4baf11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bebae04c72b934bfbbf0b4d01f164f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a951292add4574c1debd16800674e1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/3b76558d-a962-4c56-95ba-e85d81c720d3.png?resizew=116)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/710c8b60b12f8003109c1d48cdd91e0f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abe38c885f29722c433022c4b2ae6211.png)
您最近一年使用:0次
2022-12-02更新
|
761次组卷
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3卷引用:重庆市永川区永川北山中学校2022年高二上学期期中数学试题
名校
解题方法
5 . 如图,在四棱锥
,底面
为平行四边形,
为等边三角形,平面
平面
,
.
(1)设
分别为
的中点,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
平面
;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44f4120c94cb7176dc31fcac387b32e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/12/cc2762dd-0136-4d75-88be-a47f2bd49888.png?resizew=186)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f3ed5ea1cf0fa8f7c6be46cd5fa057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc9553d0fa450786b888561368b7194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2023-09-11更新
|
640次组卷
|
5卷引用:重庆市永川北山中学校2022-2023学年高一下学期期中数学试题
6 . 如图所示,在四棱锥P-ABCD中,PC⊥底面ABCD,
,
,
,E是PB的中点.
![](https://img.xkw.com/dksih/QBM/2022/1/13/2893674887897088/2895068048809984/STEM/807eedb3-7a6b-4d1b-b655-7ebf2014b56f.png?resizew=184)
(1)求证:
平面PAD;
(2)若
,求三棱锥P-ACE的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd3c2e2199cd4565c05b949bc21fc37.png)
![](https://img.xkw.com/dksih/QBM/2022/1/13/2893674887897088/2895068048809984/STEM/807eedb3-7a6b-4d1b-b655-7ebf2014b56f.png?resizew=184)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932a04304f2d4975955d4baabb2deeea.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2899e607479d8d1c47d954ae9ebb7144.png)
您最近一年使用:0次
2022-01-15更新
|
552次组卷
|
2卷引用:重庆市永川北山中学校2023届高三上学期期中数学试题