如图,在正三棱柱(底面是正三角形的直三棱柱)
中,
,D,E分别是
的中点.
![](https://img.xkw.com/dksih/QBM/2022/2/16/2917484579733504/2933026863177728/STEM/1919073f-1ccf-4c21-b585-55d7c4fa9387.png?resizew=138)
(1)求证:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c268ff5785e303b8420de92b2ef680c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13698f6fb90eb5957df14a077c567af.png)
![](https://img.xkw.com/dksih/QBM/2022/2/16/2917484579733504/2933026863177728/STEM/1919073f-1ccf-4c21-b585-55d7c4fa9387.png?resizew=138)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd87eb91c373da659934ccb01dae2b9.png)
2022·陕西西安·一模 查看更多[4]
陕西省西安市周至县2022届高三下学期一模文科数学试题(已下线)第八章 立体几何初步(章末综合卷)-2021-2022学年高一数学链接教材精准变式练(人教A版2019必修第二册)广西玉林市县级重点高中2021-2022学年高一下学期期中联考数学试题安徽省宣城中学2021-2022学年高一下学期期中数学试题
更新时间:2022-03-10 08:01:20
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解答题-问答题
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【推荐1】如图所示,在四棱锥
中,
,
,点M在线段SB上,且
平面SAD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/1d8299e5-4fae-468f-a556-1fd493f32a59.png?resizew=233)
(1)求
的值,并说明理由;
(2)若
,
,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bce559fceb4731f8d4323410075a22b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871ea1fe36ff3d2414bce1a2e507dd7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa14afe6f0aad22e8e869c39a60be657.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/1d8299e5-4fae-468f-a556-1fd493f32a59.png?resizew=233)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7679c7f87ba0d46225bad5baf15fb3af.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c3ec174b1ce835cc8737ff6ce57e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2095837b7420f07fc9ae946ece406df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
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【推荐2】如图,在直三棱柱
中,
,
,
,
,
分别为
,
,
的中点.
与平面
的位置关系,并说明理由;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b51da47ab8433342f7a319e412fefae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17d954212889c8aae3cbb84de7cb362a.png)
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【推荐1】已知
为正方体,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/10/b93385e5-8f0b-469c-8dc3-63e128ef4d61.png?resizew=212)
(1)求证:
平面
;
(2)求证:直线
平面
.
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/10/b93385e5-8f0b-469c-8dc3-63e128ef4d61.png?resizew=212)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
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【推荐2】.如图,AB是⊙O的直径,VA垂直⊙O所在的平面,点C是圆周上不同于A,B的任意一点,M,N分别为VA,VC的中点.
![](https://img.xkw.com/dksih/QBM/2020/10/23/2577112608661504/2577984993624064/STEM/33ea4106716142398be5f911b5ef0e2b.png?resizew=131)
(1)求证:MN∥平面ABC
(2)求证:BC⊥平面VAC
![](https://img.xkw.com/dksih/QBM/2020/10/23/2577112608661504/2577984993624064/STEM/33ea4106716142398be5f911b5ef0e2b.png?resizew=131)
(1)求证:MN∥平面ABC
(2)求证:BC⊥平面VAC
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