名校
解题方法
1 . 如图1所示,在边长为3的正方形
中,将
沿
折到
的位置,使得平面
平面
,得到图2所示的三棱锥
.点
分别在
上,且
,
,
.记平面
与平面
的交线为l.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/26/a232b33a-64b7-48ee-ad75-468ec615404d.png?resizew=335)
(1)在图2中画出交线l,保留作图痕迹,并写出画法.
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9524e3810e06dc781285f1289e75d653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1095b030f441de5fb223781b00f3dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bb1063e139610045f3bca5ca0b2766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715ef932b72eb703f3e7a17ee2ce6a7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1828795d52174dd64fba1c9ebe61072b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cf0ee918f8c2f753302d3b5928d358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/26/a232b33a-64b7-48ee-ad75-468ec615404d.png?resizew=335)
(1)在图2中画出交线l,保留作图痕迹,并写出画法.
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7f9eca6d2aabe3f9e0f39b46106ce4.png)
您最近一年使用:0次
2023-04-25更新
|
510次组卷
|
3卷引用:四川省南充市嘉陵第一中学2022-2023学年高二下学期期中理科数学试题
名校
2 . 如图所示,在四棱锥
中;平面
平面
,
,且
,设平面
与平面
的交线为
.
(1)作出交线
(写出作图步骤),并证明
平面
;
(2)记
与平面
的交点为
,点
在交线
上,且
,求平面
与平面
夹角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/405effb49ef901476701e72cc47918da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b214ed23a02c81f396c04c1fd83d511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/14/3beddb56-e220-4f2a-962e-e13df184cb66.png?resizew=183)
(1)作出交线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9df740160690029ac1e730c85f20347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e838fe409bbcd8fd0150e22607204ef1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc6f6dfdbe7d39891c35f67e1a95c7f.png)
您最近一年使用:0次
解题方法
3 . 如图,在直三棱柱
中,底面
是边长为4的等边三角形,且
是棱
上一动点(不包括端点),
为
的中点.
(1)若
为
的中点,请作出
与平面
的交点
,并写出
与
的比值(在图中保留作图痕迹,不必写出画法和理由);
(2)设直线
与平面
所成的角为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/067646fa32976be03cc431cda562a501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/4/ceb2e7cf-3f83-451a-a9b2-c38d840b29ec.png?resizew=157)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ef601ca1f9c4c031adab4ffed297f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b99738c0ba6ad5af08c609bd57fbc015.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5888bec948373f3854258ad80171073d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7d5ef3a3d9a03be91135fc426d57cc.png)
您最近一年使用:0次
解题方法
4 . 已知正四棱锥
中,O为底面ABCD的中心,如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/05dc9a6b-56ad-4274-a7b8-1b8fa142b1e1.png?resizew=162)
(1)作出过点O与平面PAD平行的截面,在答题卡上作出该截面与四棱锥表面的交线,写出简要作图过程及理由;
(2)设PD的中点为G,
,求AG与平面PAB所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/05dc9a6b-56ad-4274-a7b8-1b8fa142b1e1.png?resizew=162)
(1)作出过点O与平面PAD平行的截面,在答题卡上作出该截面与四棱锥表面的交线,写出简要作图过程及理由;
(2)设PD的中点为G,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
您最近一年使用:0次
2022-11-23更新
|
326次组卷
|
3卷引用:山东省潍坊市五县市2022-2023学年高二上学期期中数学试题
名校
解题方法
5 . 如图,已知正三棱柱
中,所有棱长均为2,点E,F分别为棱
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/d1da7309-f913-43e5-b38e-71b659098164.png?resizew=217)
(1)求
与平面AEF所成角的正弦值;
(2)过A、E、F三点作一个平面,则平面AEF与平面
有且只有一条公共直线,在图中作出这条公共直线,简略写清作图过程,并求这条公共直线在正三棱柱底面
内部的线段长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/d1da7309-f913-43e5-b38e-71b659098164.png?resizew=217)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
(2)过A、E、F三点作一个平面,则平面AEF与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
您最近一年使用:0次
6 . 舒腾尺是荷兰数学家舒腾设计的一种作图工具,如图,O是滑槽AB的中点,短杆ON可绕O转动,长杆MN通过N处的铰链与ON连接,MN上的栓子D可沿滑槽AB滑动.当点D在滑槽AB内做往复移动时,带动点N绕O转动,点M也随之而运动.记点N的运动轨迹为
,点M的运动轨迹为
.若
,
,过
上的点P向
作切线,则切线长的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54298f581688081d0b0214334a0dedf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e47bb98258ebfcf1d8ad4bac10b7ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,直四棱柱
的底面
为直角梯形,
,
,
,
,
、
分别为棱
、
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/e41ff8de-2807-44bc-a978-37a601f7a5b6.png?resizew=183)
(1)在图中作出平面
与该棱柱的截面图形,并用阴影部分表示(不必写出作图过程);
(2)
为棱
的中点,求异面直线
与
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6037bba27008abc96a6dba99753549ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da9db73dad37a8a07a7ccc49101db545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d262480ffb55b7617f44b63f130c154a.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/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/e41ff8de-2807-44bc-a978-37a601f7a5b6.png?resizew=183)
(1)在图中作出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8035fc825a001d7d9a3dacd8271662.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dd5b5d9bed01632b26ab881deab2afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,直四棱柱
的底面
为直角梯形,
,
,
,
,
,
分别为棱
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/25/0eeb0e30-ea01-43c9-8107-1f89ea74f8f1.png?resizew=211)
(1)在图中作出平面
与该棱柱的截面图形,并用阴影部分表示(不必写出作图过程);
(2)
为棱
的中点,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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258f8e9f45a2b3e11d1513f23315feeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d262480ffb55b7617f44b63f130c154a.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/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/25/0eeb0e30-ea01-43c9-8107-1f89ea74f8f1.png?resizew=211)
(1)在图中作出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcf0dadb80d0d4201cc4fd16479b7d9.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dd5b5d9bed01632b26ab881deab2afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
您最近一年使用:0次
2020-09-16更新
|
700次组卷
|
2卷引用:辽宁省大连市第一中学2021-2022学年高二上学期10月月考数学试题
名校
解题方法
9 . 在正方体中,
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/31/24a9bce2-7d5f-42f1-8210-4c66c9c498ec.png?resizew=161)
(1)作出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc725182c2fd1413319fea35b95c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42b4e11e3d0c9f18c4f7bdc9404824e.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,四边形
是正方形,
平面
,
,
,
在线段
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/dee0013d-4a39-4b68-af36-65913fee0109.png?resizew=141)
(1)若
平面
,请在图中画出点
,保留作图痕迹,并说明理由.
(2)是否存在点
,使得
与平面
所成角的正弦值为
,若存在,求出
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed04b01505bbd8a4ac0bc12e46f23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180868535d96d800625148a03a33e9d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bcf55cb4ea16c17f20e02190ffdff07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/dee0013d-4a39-4b68-af36-65913fee0109.png?resizew=141)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d30788a482598e638aea779ac14da12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df5935c893580c77ab6fa6eb0a70bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83303d3784492506fc44f2b4d6b07bc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383c681f398877a4589a389d19a0f2e6.png)
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