1 . 如图多面体ABCDEF中,面
面
,
为等边三角形,四边形ABCD为正方形,
,且
,H,G分别为CE,CD的中点.
;
(2)求平面BCEF与平面FGH所成角的余弦值;
(3)作平面FHG与平面ABCD的交线,记该交线与直线AD交点为P,写出
的值(不需要说明理由,保留作图痕迹).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1056cd2db035cbfcce4935ffec20030a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eaceb8d6c6927e14d9ac7a557a2b11d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee73452ee4d5437f1399f1235b95e55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36896e2033dd49401aca07a4a1e1d267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b9d0c688e55286443c9974797fc647f.png)
(2)求平面BCEF与平面FGH所成角的余弦值;
(3)作平面FHG与平面ABCD的交线,记该交线与直线AD交点为P,写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb5391d00655e9e4ee30fe9934b2f02c.png)
您最近一年使用:0次
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解题方法
2 . 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:辽宁省多校联盟2019-2020学年高一下学期数学期末试题
解题方法
3 . 用平行于圆锥底面的平面截圆锥,截面与底面之间的几何体称为圆台,也可称为“截头圆锥”.在如图的圆台
中,上底面半径为
,下底面半径为
,母线长为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/dcbeb60f-10fe-4a9c-862d-16cfa7d0a6b9.png?resizew=177)
(I)结合圆台的定义,写出截面
的作图过程;
(II)圆台截面
与截面
是两个全等的梯形,若
,求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbe2aba242716238b79c46bb1f40e88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/dcbeb60f-10fe-4a9c-862d-16cfa7d0a6b9.png?resizew=177)
(I)结合圆台的定义,写出截面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(II)圆台截面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bebae04c72b934bfbbf0b4d01f164f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213d25b5ade550ec6afd3536e9eb5d75.png)
您最近一年使用:0次
名校
解题方法
4 . 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: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
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
5 . 如图,已知正方体
的上底面内有一点
,点
为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/acc4fb82-f5ef-4449-b4f4-46e21dee4b20.png?resizew=176)
(1)经过点
在上底面画一条直线
与
垂直,并说明画出这条线的理由;
(2)若
,求
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/acc4fb82-f5ef-4449-b4f4-46e21dee4b20.png?resizew=176)
(1)经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bde6d6ab9706c59659c1f16f415825d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7865126ef23077f3ed6832899a600732.png)
您最近一年使用:0次
2021-11-08更新
|
312次组卷
|
2卷引用:辽宁省沈阳市翔宇中学2021-2022高三上学期第二次月考数学试题
解题方法
6 . 已知等腰直角
,
,点
,
分别为边
,
的中点,沿
将
折起,得到四棱锥
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/2021/4/14/2699832628871168/2699847332904960/STEM/0fe4285d410041fbb38cb9acb0eb5b86.png?resizew=405)
(Ⅰ)过点
的平面
平面
,平面
与棱锥
的面相交,在图中画出交线;设平面
与棱
交于点
,写出
的值(不必说出画法和求值理由);
(Ⅱ)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e49817548cb45b3d1e58570644c6fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fda85608d705caa6eff2bed57113759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c009f663ad2b0c3ba521daf4b86b066f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235d1553f6806c1eee3b17b94d23f0f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2021/4/14/2699832628871168/2699847332904960/STEM/0fe4285d410041fbb38cb9acb0eb5b86.png?resizew=405)
(Ⅰ)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414844edd458857bdfc80bffa61cbf9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b98851cd97e52ae204272ab60a0a4c.png)
(Ⅱ)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda0f75d56aa1571a0839619ffe21fed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
您最近一年使用:0次
2021-04-14更新
|
683次组卷
|
3卷引用:东北三省四市教研联合体2021届高三第二次联合考试理科数学试题
东北三省四市教研联合体2021届高三第二次联合考试理科数学试题东北三省三校(哈师大附中、辽宁省实验中学、东北师范大学附属中学)2021届高三二模数学(理)试题(已下线)专题2.7 空间向量与立体几何-2021年高考数学解答题挑战满分专项训练(新高考地区专用)
7 . 已知四棱锥
中,底面
为菱形,且
,
,过侧面
中线
的一个平面
与直线
垂直,并与此四棱锥的面相交,交线围成一个平面图形.
(1)画出这个平面图形,并证明
平面
;
(2)若
,求平面
与平面
所成的锐二面角的余弦值.
![](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/051f092cbf89536d7e8b9fbf9d49355d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f59675193ae3ad89cc93503cf095a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e2903ff33266528a7902ad51cf8d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
(1)画出这个平面图形,并证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d0710321d97361e5782124bbf7f0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
8 . 已知在四棱
中,底面ABCD是矩形,且
,
,
平面ABCD,F是线段BC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/ab8036f9-037e-4c19-8846-aec9740008c7.png?resizew=174)
求证:
;
若直线PB与平面ABCD所成的角为
,求二面角
的余弦值;
画出平面PAB与平面PDF的交线
不写画法
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf3746205daae4787d8e31d74ba79e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a9fa8832f98b5418a7d75892f7951b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4564baf209de77802d46cda82995c5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/ab8036f9-037e-4c19-8846-aec9740008c7.png?resizew=174)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce847eb2a8460d02086d1620862039.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe8140a38ee6b0b28a5b661f8b1f3d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8451f5b9076c0403b3f028cef6a0ad5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bb89a362c1faf4d0c306eabbb59710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4159efe71dae51f63f5b407f88fb8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
您最近一年使用:0次
9 . 已知长方体
中,
,
,
为
的中点,如图所示.
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101202432/STEM/49456572f1ee42cb9541659967d8bb72.png)
(1)在所给图中画出平面
与平面
的交线(不必说明理由);
(2)证明:
平面
;
(3)求平面
与平面
所成锐二面角的大小.
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101202432/STEM/c75aa33c70d84d6888d11ba35632150f.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101202432/STEM/daf735d3e0e24ba2bb20fe187cf798d4.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101202432/STEM/8bb972e6229d421da434a47ab5c0526e.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101202432/STEM/8971dbe6938748ff8c1cbc4634d3b6fe.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101202432/STEM/b8fb13f4cbae4dd6b07821fa8a95400d.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101202432/STEM/49456572f1ee42cb9541659967d8bb72.png)
(1)在所给图中画出平面
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101202432/STEM/a5ac56a353e743eebd7a75199c412bd2.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101202432/STEM/c83c5e60d0f14f00ac428bd983f25392.png)
(2)证明:
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101202432/STEM/a9807f9890f3403d8301b48647d0a3c0.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101202432/STEM/c83c5e60d0f14f00ac428bd983f25392.png)
(3)求平面
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101202432/STEM/a5ac56a353e743eebd7a75199c412bd2.png)
![](https://img.xkw.com/dksih/QBM/2016/12/23/1619431100727296/1619431101202432/STEM/c83c5e60d0f14f00ac428bd983f25392.png)
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2016-12-04更新
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576次组卷
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2卷引用:2016届辽宁省沈阳市高三教学质量监测一理科数学试卷