解题方法
1 . 如图,在多面体
中,四边形
是直角梯形,
,
,
,
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/beaac8de-694f-4795-ade3-366852fe4428.png?resizew=158)
(1)证明:
平面
.
(2)若
,求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed619e2dc900c52a29012e5b821451bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b28bf7a1162221c19758f421f012650.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/beaac8de-694f-4795-ade3-366852fe4428.png?resizew=158)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75aea24647cd4d0b4b9aa513bf5457b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8fe122a768a4d78b5b39817d557a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
您最近一年使用:0次
名校
2 . 如图所示,在三棱柱
中,
,点
在平面
的射影为线段
的中点,侧面
是菱形,过点
、B,D的平面
与棱
交于点E.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/631e9b44-e123-41f6-b1ec-0ec73c275a27.png?resizew=162)
(1)在图中作出截面
,并证明四边形
为矩形;
(2)若
,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/631e9b44-e123-41f6-b1ec-0ec73c275a27.png?resizew=162)
(1)在图中作出截面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/202794c51b2166eca170da9c53247bea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/202794c51b2166eca170da9c53247bea.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd4c85bb98a2a0afddd7ed92578ad2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
您最近一年使用:0次
解题方法
3 . 如图,在棱长为2的正方体
中,
,
,
,
分别为
,
,
,
的中点,点
为线段
上的动点,且
.
![](https://img.xkw.com/dksih/QBM/2021/7/8/2759898787160064/2778264566128640/STEM/5f2d6e941fa345d5a6ed8508d4498d6e.png?resizew=155)
(1)是否存在
使得
平面
,若存在,求出
的值并给出证明过程;若不存在,请说明理由;
(2)画出平面
截该正方体所得的截面,并求出此截面的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faf7d52ab2f7e07f0a451a35ac23e22a.png)
![](https://img.xkw.com/dksih/QBM/2021/7/8/2759898787160064/2778264566128640/STEM/5f2d6e941fa345d5a6ed8508d4498d6e.png?resizew=155)
(1)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5311bb2a8564c3ff0d683d443633f746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)画出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
您最近一年使用:0次
2021-08-03更新
|
817次组卷
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5卷引用:福建省安溪一中、养正中学、惠安一中、泉州实验中学2021-2022学年高一下学期期中数学试题
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