名校
1 . 如图甲,在菱形
与等腰直角
中,
,
,
,现将
沿
旋转,点
旋转到点
,如图乙,若
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/ff4d58a3-3259-46de-857c-c3f8cbda9eeb.png?resizew=315)
(1)求证:
;
(2)求二面角
平面角的余弦的绝对值,并据此求出平面
在平面
上投影的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c1c122603b60b6f1a1334ddb56c3fb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3755b2bcf7516eedb26a27ad73657216.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/ff4d58a3-3259-46de-857c-c3f8cbda9eeb.png?resizew=315)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbd1316b9d1f0c1e71fd078deec61f6.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
名校
解题方法
2 . 已知直角梯形形状如下,其中
,
,
,
.
(1)在线段CD上找出点F,将四边形
沿
翻折,形成几何体
.若无论二面角
多大,都能够使得几何体
为棱台,请指出点F的具体位置(无需给出证明过程).
(2)在(1)的条件下,若二面角
为直二面角,求棱台
的体积,并求出此时二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7972619832ab08705c12f2486aa13602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/5/89d10d27-7a5c-4999-b048-68bb095d4ed3.png?resizew=375)
(1)在线段CD上找出点F,将四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08c14e87a2bcf7090eab2fea73667d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc6a1a01fdb186620b7939c789fb8bf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab64d1bfb556d9c529f867b9c83ad67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc6a1a01fdb186620b7939c789fb8bf3.png)
(2)在(1)的条件下,若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab64d1bfb556d9c529f867b9c83ad67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc6a1a01fdb186620b7939c789fb8bf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd22fa132fa5c914b527c2781a516049.png)
您最近一年使用:0次
2023-06-03更新
|
713次组卷
|
3卷引用:云南省三校2023届高三数学联考试题(八)
名校
解题方法
3 . 如图所示的几何体为一个正四棱柱被两个平面
与
所截后剩余部分,且满足
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/13/1477b758-6170-42d8-b055-c1aacdcbecac.png?resizew=185)
(1)当
多长时,
,证明你的结论;
(2)当
时,求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72406478fda1c6e3b8052467385a3bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09219dbd440c70d66bf2bf8b4c2bfe2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46264ad39c95ef05658e3fa15373c6d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37cb657446616b7d679dfd9d2bbef5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2743a47b0c3e422512b4c76cc7112232.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/13/1477b758-6170-42d8-b055-c1aacdcbecac.png?resizew=185)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79216c6a32bb699aeb36144da020490.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51bb339ba41929e8f693b3618d5ee4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72406478fda1c6e3b8052467385a3bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09219dbd440c70d66bf2bf8b4c2bfe2f.png)
您最近一年使用:0次
2023-03-10更新
|
922次组卷
|
4卷引用:云南省文山州广南县第一中学校2024届高三上学期第一次省统测数学模拟试题
名校
4 . 三棱锥
中,
,
,
,直线
与平面
所成的角为
,点
在线段
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/1401ce1c-58c3-4119-8bb6-4cd452cd97c2.png?resizew=160)
(1)求证:
;
(2)若点
在
上,满足
,点
满足
,求实数
使得二面角
的余弦值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/463c7753d6f7614f90b19245bb3e439e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1affed1ad8e53a73308c85849a72444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbb05b8b630052ff544249ebd72d95d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/1401ce1c-58c3-4119-8bb6-4cd452cd97c2.png?resizew=160)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70734a8e672376bb0bd1522e229f86a2.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bb04187b181054c7ddc7f0e35e3e5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c49e8906f0de208b36a18e448f7ecc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445b51117626fbd3373e32acc514c64b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33adb74906403b0b00fcbd9fa691d8b.png)
您最近一年使用:0次
2022-01-21更新
|
667次组卷
|
4卷引用:云南省保山市腾冲市第八中学2023-2024学年高二上学期期末模拟数学试题
5 . 如图1,在
中,
,点
,D是
的三等分点,点
,C是
的三等分点.分别沿
和DC将
和
翻折,使平面
平面ABCD,且
平面ABCD,得到几何体
,作
于E,连接AE,
,如图2.
![](https://img.xkw.com/dksih/QBM/2022/3/28/2946061805494272/2946802715672576/STEM/5ee0ac8f-3164-4f23-b39a-2b18e55860c2.png?resizew=234)
(1)证明:图2中,
;
(2)在图2中,若
,求直线
与平面ADE所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3c5f5006941a576a60a9a0a8a40f3f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad16665c5d47ce756cc2980423bf4b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbafedc202bd0d86c4dfdece9f8f4fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eee50e904fed4ad9c6292bec0b08a8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab01dbac75a51c89c9d44395cd649985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be34fcb7a3e3face28003b7015a5b3cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddbb0422a136f45653c8c369f2d75fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52eab6de89f4d4e69650e94e0968744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1992c4aaf4b709b7be1d0de58c2e119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://img.xkw.com/dksih/QBM/2022/3/28/2946061805494272/2946802715672576/STEM/5ee0ac8f-3164-4f23-b39a-2b18e55860c2.png?resizew=234)
(1)证明:图2中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67baffab4177197abf8668569aad656.png)
(2)在图2中,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f7b7aef85de2d4babbc025d4329007.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75d14708e6aa1404477db9d7e3166f0.png)
您最近一年使用:0次
6 . 某建筑物的上层框图如图所示,其上下底面是平行的两正方形,上下底面的中心连线垂直于上下地面,且各侧棱均相等(即为正棱台),经测量得知
,侧棱长为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/7b28e486-08db-4c9b-b922-fcffe281bd16.png?resizew=265)
(1)求证
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c1060dbf8c1a85848754e0717799793.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcf43ba416adeb723cebe4aee6bbe34.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/7b28e486-08db-4c9b-b922-fcffe281bd16.png?resizew=265)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1de5964353beb55c5058b2a431eecaf.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b6ab5a1695a47751d93ec248ee61eaa.png)
您最近一年使用:0次
解题方法
7 . 如图,将等腰直角
沿斜边
旋转,使得
到达
的位置,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/b700e49f-33b5-46cf-8904-120b3bf6d21b.png?resizew=157)
(1)证明:平面
平面
.
(2)求二面角
的余弦值.
(3)若在棱
上存在点
,使得
,
,在棱
上存在点
,使得
,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90f9fba63790e1e5308fa5a1441d71a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/b700e49f-33b5-46cf-8904-120b3bf6d21b.png?resizew=157)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae50ff4c814b581a78346e548964aae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00f1eaa084baa5272450c34ab1ffde54.png)
(3)若在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffb952f86442845da723fd291564484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb1a61e889d0b83ed95a38f1adf4e8e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077ad2164c272a0ca4c52f3159b0e486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5987b311288bb1f71556dfe81d936c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79498e1df1280868532f59ee8059a223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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