名校
解题方法
1 . 已知四棱锥
,底面
为矩形,
,
,
分别是
,
,
的中点.证明:
平面
;
(2)
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/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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de22059d7d80f24817235269e9bb1ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12d8677ae5ca7acf874d93789425d172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
您最近一年使用:0次
解题方法
2 . 如图,在四棱锥
中,AB
CD,
,过点E的平面与棱PC,PD,AD分别交于点F、H、G,且平面PAB
平面EFHG.
![](https://img.xkw.com/dksih/QBM/2022/4/21/2963034939473920/2965905794760704/STEM/215a67a7b2ef47958b197d0611a8fb45.png?resizew=214)
(1)求证:EG
平面PDC;
(2)若
平面
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02dd7f88976eb5975d31b410d0d973.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://img.xkw.com/dksih/QBM/2022/4/21/2963034939473920/2965905794760704/STEM/215a67a7b2ef47958b197d0611a8fb45.png?resizew=214)
(1)求证:EG
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dcff7d412c9568b98825fac3e7715a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aea07c88ff1e9b187461b780535dcd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec66c1d36c6c2be3d3fc4519dfca195e.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,在正方体
中,
,
、
、
分别为
、
、
中点.
![](https://img.xkw.com/dksih/QBM/2021/7/10/2761063105978368/2762750064877568/STEM/71751841a9a24692b6a568b6f9bafd33.png?resizew=241)
(1)求证:
平面
;
(2)求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/2021/7/10/2761063105978368/2762750064877568/STEM/71751841a9a24692b6a568b6f9bafd33.png?resizew=241)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b859ca54ab085edf70c1179a7d103a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
您最近一年使用:0次
2021-07-12更新
|
2250次组卷
|
2卷引用:重庆市南开中学校2020-2021学年高一下学期期末数学试题
4 . 如图,在直三棱柱
中,点
、
分别为
和
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/dc67479f-01e4-4abd-8307-1cf201bdd9ea.png?resizew=201)
(1)证明:
平面
;
(2)若
,
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.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/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/dc67479f-01e4-4abd-8307-1cf201bdd9ea.png?resizew=201)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d355b4c58b4e883b9e65cc6da8622e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e384e0ffc3d599303b77ee2a12221e.png)
您最近一年使用:0次
2020-09-25更新
|
932次组卷
|
3卷引用:四川省巴中市2021届高三零诊考试数学(理)试题
名校
解题方法
5 . 如图,四棱锥
中,平面
平面
,底面
为梯形,
,
,
.且
与
均为正三角形,
为
的中点,
为
重心.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/c31a9809-e239-40f1-92b7-64a2583977ca.png?resizew=175)
(1)求证:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8cfaf72b97aa690ff41c84f9ed29a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0d5f57a40474205aee752e23ec449d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/c31a9809-e239-40f1-92b7-64a2583977ca.png?resizew=175)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf60ad9db3411f35704fa88d86bfef5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c440fdd6a9db8fcbf6584dd03d0140a6.png)
您最近一年使用:0次
2020-05-31更新
|
267次组卷
|
2卷引用:江西省南昌市进贤县第一中学2019-2020学年高二下学期开学考试数学(文)试题
解题方法
6 . 如图,四棱锥
的底面
是边长为2的正方形,
平面
,
,
分别是棱
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/d863e2d7-5c18-4c47-af3f-ece955bd51b4.png?resizew=194)
(1)求证:
平面
;
(2)若
,求平面
将三棱锥
分成的两部分的体积中较大部分的体积.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/d863e2d7-5c18-4c47-af3f-ece955bd51b4.png?resizew=194)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c482ee1668a59ca21f3ae8b6bad58eae.png)
您最近一年使用:0次
解题方法
7 . 如图,正方体
的棱长为
,点
、
为棱
、
的中点.
![](https://img.xkw.com/dksih/QBM/2020/4/26/2449798289408000/2450436423729152/STEM/69b52571e55c412dad4f29de4666e242.png?resizew=220)
(1)求证:
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e19d1a7e89beddaf468bdce5e31550e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e737bc35da650eda3825d29799b5f86f.png)
![](https://img.xkw.com/dksih/QBM/2020/4/26/2449798289408000/2450436423729152/STEM/69b52571e55c412dad4f29de4666e242.png?resizew=220)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f70cf3f6c7acbf60d4a4ca0ce89619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe02a25afc35da213ba4aee378a308b.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4171e7f713d6b265d56b2662b7af57b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
您最近一年使用:0次
名校
解题方法
8 . 如图为一简单组合体,其底面
为正方形,
平面
,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/058095b0-2433-4399-942f-e50acc60d8cf.png?resizew=146)
(1)求四棱锥
的体积;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b73f874048f9e48ae35ee95bbf443bce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a6e07a3ef8f3969afb82f91e6ae4ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/058095b0-2433-4399-942f-e50acc60d8cf.png?resizew=146)
(1)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086d11e84f892311b5f4a5c306f859cc.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7175df06e33cad4e6bbc3f2f6b0a2986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564376a88fa74090de9f7694226a6184.png)
您最近一年使用:0次
2020-03-20更新
|
1013次组卷
|
3卷引用:2020届黑龙江省海林市朝鲜族中学高三上学期期末数学(文)试题
19-20高二·浙江·期末
名校
9 . 如图所示四棱锥
中,
底面
,四边形
中,
,
,
,
,
为
的中点,
为
中点.
![](https://img.xkw.com/dksih/QBM/2020/3/5/2412911289155584/2412954668687360/STEM/a3dbb57fb4c84ffa84bec7b9146a0a4c.png?resizew=223)
(1)求证:
平面
;
(2)求直线
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/d5acb763021bf166ca719d07223591d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81981fd7b343f4fe2db8f36eb66c1ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2020/3/5/2412911289155584/2412954668687360/STEM/a3dbb57fb4c84ffa84bec7b9146a0a4c.png?resizew=223)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8ccd4181f956f6e0140bf0ab8f0716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
2020-03-05更新
|
476次组卷
|
4卷引用:【新东方】新东方高二数学试卷304
解题方法
10 . 如图,在三棱柱
中,侧面
是菱形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/580c26c8-4fa1-4c2d-b693-b145c353c783.png?resizew=182)
(1)若
是线段
的中点,求证:平面
平面
;
(2)若
、
、
分别是线段
、
、
的中点,求证:直线
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d89ba4036a5d18ec4abed44d7fd8e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/064a04589ae680482d23c3b08f820917.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/580c26c8-4fa1-4c2d-b693-b145c353c783.png?resizew=182)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbbfeda651af6a71a11f4bef378055c4.png)
(2)若
![](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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd4c85bb98a2a0afddd7ed92578ad2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
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