解题方法
1 . 如图,在四棱锥
中,
,
,
,AB=AC=2,AE=ED=1.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/1b66493c-c26b-4f22-87d8-9c5efe2a5712.png?resizew=171)
(1)若F为AC中点,G为AB中点,
,求证:
平面BCD;
(2)若平面
平面ABC,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f9045e6cd575bbe76c89ef6ef852fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7bd02e0adeae92ba9526261b1baf797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032b3e422eeb39cf649dffc9934a7cf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/1b66493c-c26b-4f22-87d8-9c5efe2a5712.png?resizew=171)
(1)若F为AC中点,G为AB中点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c97a7fab5d1550e2fef66772cc985fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5d62dcf1c173fe35595dfed43f9c87.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31effd1d3f7ce1f6e57be80c7f3af4ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b9fac14c8330781420fa076b2e04e77.png)
您最近一年使用:0次
2 . 如图,在四棱锥
中,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/2/1bdb9ab3-806f-46dc-924c-05ee2176642a.png?resizew=196)
(1)若
为
中点,
为
中点,
,求证:
平面
;
(2)若平面
平面
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f9045e6cd575bbe76c89ef6ef852fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7bd02e0adeae92ba9526261b1baf797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032b3e422eeb39cf649dffc9934a7cf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5590d0226850c341940e6d9cbab180bf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/2/1bdb9ab3-806f-46dc-924c-05ee2176642a.png?resizew=196)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](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/5c97a7fab5d1550e2fef66772cc985fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2cb00dc421f44e30228aa26a532582c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31effd1d3f7ce1f6e57be80c7f3af4ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/324d453870b345da0c41977290192f94.png)
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名校
3 . 如图,在等腰直角三角形
中,
分别是
上的点,且
分别为
的中点,现将
沿
折起,得到四棱锥
,连接![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23853b5555468f9d803713d1d9353750.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/3e6740be-3953-4f28-91ea-930c1735e3f6.png?resizew=400)
(1)证明:
平面
;
(2)在翻折的过程中,当
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084ce748ea72556d4d575d84d0ea594f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc6b04dcd5a34b8125696faf552ab63f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79c1b3d8a1ea4d9370996706199e5a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0fa96c746ceab61c043cbb95b7d2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357265c532428e886a643e8e653eec9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23853b5555468f9d803713d1d9353750.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/3e6740be-3953-4f28-91ea-930c1735e3f6.png?resizew=400)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)在翻折的过程中,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1069d514c3c32aeabd274475ee209ed6.png)
您最近一年使用:0次
2022-06-18更新
|
1513次组卷
|
11卷引用:安徽省淮南一中2020-2021学年高二下学期开学考理科数学试题
安徽省淮南一中2020-2021学年高二下学期开学考理科数学试题安徽省江淮名校2020-2021学年高二下学期开学联考数学(理)试题吉林省松原市宁江区吉林油田高级中学2021-2022学年高二上学期期初数学考试试题陕西省西安市长安区第一中学2020-2021学年高二上学期期末数学(理)试题湖北省宜昌市示范高中教学协作体2021-2022学年高二上学期期中数学试题(已下线)专题9.10—立体几何—二面角2—2022届高三数学一轮复习精讲精练贵州省遵义市第五中学2021-2022学年高二上学期期中考试数学(理)试题福建省福州第一中学2021-2022学年高一下学期期末考试数学试题(已下线)专题24 立体几何解答题最全归纳总结-1(已下线)第07讲 向量法求距离、探索性及折叠问题 (练)(已下线)1.2.4 二面角
4 . 如图,在长方体
中,
,
,
为
的中点. 平面
与棱
交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/959426eb-2972-4c04-bebd-9c4a54495871.png?resizew=197)
(1)证明:
平面
;
(2)点
为棱
上一点,且
,求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1880586c33da315e49ccb6e2d531c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/547cd9827c177154eeb6caf1a0148144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/959426eb-2972-4c04-bebd-9c4a54495871.png?resizew=197)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/119b3495eb725bd06e865fa9c77ff74d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb37f1ec8a370e5136e69f9fef73dae8.png)
您最近一年使用:0次
名校
5 . 如图所示,在四棱锥
中,底面四边形
是菱形,底面
是边长为2的等边三角形,PB=PD=
,AP=4AF
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/a93bb600-1ac6-48dc-b699-8a170222ee71.png?resizew=209)
(1)求证:PO⊥底面ABCD
(2)求直线
与OF所成角的大小.
(3)在线段
上是否存在点
,使得
平面
?如果存在,求
的值;如果不存在,请说明理由.
![](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/1fa0c1a6e9990d435f5df2cba32cc203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/a93bb600-1ac6-48dc-b699-8a170222ee71.png?resizew=209)
(1)求证:PO⊥底面ABCD
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5865d488a9cf1181016fd2e866177cdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8180b12d96caf2e6b3ca28a474185e41.png)
您最近一年使用:0次
2020-12-05更新
|
2359次组卷
|
11卷引用:江西省南昌市豫章中学2021-2022学年高二入学调研(B)数学(理)试题
江西省南昌市豫章中学2021-2022学年高二入学调研(B)数学(理)试题新疆新源县2020-2021学年高一下学期期末联考数学试题四川省遂宁市射洪中学2021-2022学年高二上学期第一次月考数学理试题四川省遂宁中学校2021-2022学年高二上学期期中考试数学(文)试题河南省温县第一高级中学2021-2022学年高二上学期12月月考文科数学试题四川省遂宁市安居区2020-2021学年高二上学期期中考试数学(文)试题上海市南洋模范中学2022-2023学年高二上学期期中数学试题上海市向明中学2022-2023学年高二上学期10月月考数学试题四川省巴中市恩阳区2022-2023学年高二上学期期中数学试题新疆哈密市第八中学2021-2022学年高二上学期期末数学(理)试题(已下线)期中测试卷01(测试范围:第10-11章)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)
6 . 如图,六面体
中,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/c7aa7474-a02a-4d64-bfe4-1e3f846e5897.png?resizew=240)
(1)求证:
;
(2)若
,平面
平面
,
,
,
,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a0c3a4e61b97fa9bc58f3179fc2958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04de6e3d84ddf7da3dc4fab26e59df46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/c7aa7474-a02a-4d64-bfe4-1e3f846e5897.png?resizew=240)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab79d395d5aa7500d0606dd94b6319ff.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce726bceb02452bb4e5ed6b00fa94e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5628323a7eeb11213df5c9048b3543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb3ce43d216ad9d22ccfa0ec656266ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/940078c89bad1724a5d7006a54755398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53509459aad2e9f59f412f43b6f775d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d31815b1f3bcb36edacb318c198f41d4.png)
您最近一年使用:0次
2020-12-08更新
|
384次组卷
|
2卷引用:安徽省六安市第一中学2020-2021学年高二下学期开学考试数学(文)试题
19-20高二·浙江·期末
名校
7 . 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:海南省三亚华侨学校(南新校区)2020-2021学年高二下学期开学考试数学试题