解题方法
1 . (1)如图1,点A在直线l外,仅利用圆规和无刻度直尺,作直线
(保留作图痕迹,不需说明作图步骤).
(2)证明:一簇平行直线被椭圆所截弦的中点的轨迹是一条线段(不含端点);
(3)如图2是一个椭圆C,仅利用圆规和无刻度直尺,作出C的两个焦点,简要说明作图步骤(只说明作图步骤).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d63989923cff8efb6d67070be48794.png)
(2)证明:一簇平行直线被椭圆所截弦的中点的轨迹是一条线段(不含端点);
(3)如图2是一个椭圆C,仅利用圆规和无刻度直尺,作出C的两个焦点,简要说明作图步骤(只说明作图步骤).
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/1cc29044-247d-4d10-a2ed-edcd5f41007d.png?resizew=222)
您最近一年使用:0次
解题方法
2 . 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
名校
3 . 如图所示,在四棱锥
中,平面
平面
,
,且
,设平面
与平面
的交线为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/28/8c56d121-58e6-4ca5-9939-aa09beb56611.png?resizew=194)
(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S在交线
上,且
,当二面角
的余弦值为
,求
的值.
![](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/2023/4/28/8c56d121-58e6-4ca5-9939-aa09beb56611.png?resizew=194)
(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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e3afb50f7df3c6eb91949c8cee166bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bef3a2b3b1ca1a8dce50114e893599e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa42621cd6793e7f3673fdb49bc3123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2023-04-26更新
|
621次组卷
|
4卷引用:福建省泉州市2022届高三高考考前推题适应性练习数学试题
福建省泉州市2022届高三高考考前推题适应性练习数学试题福建省泉州市晋江市养正中学2023届高三上学期第二次月考数学试题(已下线)河北省石家庄市2023届高三质量检测(一)数学试题变式题17-22(已下线)重难点12 立体几何必考经典解答题全归类【九大题型】
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,正方体
的棱长为
分别为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/478dce1e-1612-4f04-96c4-020d8b8e0da0.png?resizew=161)
(1)请在正方体的表面完整作出过点
的截面,并写出作图过程;(不用证明)
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b684d2e78a0eb1b406913f2730e1d226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5307e04a84a0621e4d5bd2aaa1980ef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/478dce1e-1612-4f04-96c4-020d8b8e0da0.png?resizew=161)
(1)请在正方体的表面完整作出过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6f5c5097e8b1f6c46b744ea1630d41e.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/378daab67e7e1d1542e6e25f0f259185.png)
您最近一年使用:0次
2024-03-07更新
|
504次组卷
|
4卷引用:甘肃省部分学校2024届高三下学期2月开学考试数学试题
甘肃省部分学校2024届高三下学期2月开学考试数学试题河南省九师联盟2024届高三上学期2月开学考试数学试卷(已下线)重难点6-2 空间几何体的交线与截面问题(8题型+满分技巧+限时检测)内蒙古自治区赤峰市松山外国语学校2024届高三下学期开学考试数学(理)试题
名校
解题方法
6 . 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
7 . 如图,正四面体
,
(1)找出依次排列的四个相互平行的平面
,
,
,
,使得
,且其中每相邻两个平面间的距离都相等.请在答卷上作出满足题意的四个平面,并简要说明并证明作图过程;
(2)若满足(1)的平面
,
,
,
中,每相邻两个平面间的距离都为1,求该正四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495fbf56b3023539b59f7bcee29acc70.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/21fc98e1-5dbe-46a9-9c60-2bb1802386ea.png?resizew=167)
(1)找出依次排列的四个相互平行的平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943b765718479c160ba61ec5c6f8c5f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e29bf5652f0d4f764c3606efcdb445f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9177f43add5ca8480daa636afc5862b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a56eca8dc73a0e8f0c6d3a41bb26bb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109c658897735fce605120061c38709d.png)
(2)若满足(1)的平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943b765718479c160ba61ec5c6f8c5f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e29bf5652f0d4f764c3606efcdb445f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9177f43add5ca8480daa636afc5862b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a56eca8dc73a0e8f0c6d3a41bb26bb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495fbf56b3023539b59f7bcee29acc70.png)
您最近一年使用:0次
名校
解题方法
8 . 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
9 . 如图,已知多面体EABCDF的底面ABCD是边长为2的正方形,
,
,且
.
(1)记线段
的中点为
,在平面
内过点
作一条直线与平面
平行,要求保留作图痕迹,但不要求证明;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e04eb87d1aa3784c08f3239d4ff99e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a060f4fc2c8034b08c77c065f9e125d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1316f4183e8854d38283b716e2ba1b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/18/163f8856-84f6-45d9-95fa-fa04563ea83d.png?resizew=139)
(1)记线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f636f76d550dfb593a25eb680cff556.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f636f76d550dfb593a25eb680cff556.png)
您最近一年使用:0次
2023-06-15更新
|
597次组卷
|
9卷引用:广西桂林市桂林中学2017届高三5月全程模拟考试数学(理)试题
广西桂林市桂林中学2017届高三5月全程模拟考试数学(理)试题山西省太原市第五中学2017届高三第二次模拟考试(5月) 数学(理)试题辽宁省鞍山市第一中学2018届高三上学期第二次模拟考试(期中)数学(理)试题天津市实验中学2018届高三上学期第二次模拟数学(理)试题江西省临川二中、新余四中2018届高三1月联合考试数学(理)试题安徽省舒城中学2023届高三仿真模拟卷(三)数学试题(已下线)重难点突破06 立体几何解答题最全归纳总结(九大题型)-2(已下线)专题15 立体几何解答题全归类(9大核心考点)(讲义)-1(已下线)重难点12 立体几何必考经典解答题全归类【九大题型】
名校
解题方法
10 . 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)
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