2014高三·全国·专题练习
名校
解题方法
1 . 如图,在四棱锥
中,底面
是边长为
的正方形,侧面
底面
,且
,若
、
分别为
、
的中点,求证:
![](https://img.xkw.com/dksih/QBM/2022/3/28/2945825533640704/3000684830597120/STEM/885421cd9f364e55b187dfeb967bfa3e.png?resizew=209)
(1)
侧面
;
(2)
平面
.
![](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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b7201f9eb7e7c10042c096e0c9f15c.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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/2022/3/28/2945825533640704/3000684830597120/STEM/885421cd9f364e55b187dfeb967bfa3e.png?resizew=209)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
您最近一年使用:0次
2022-06-13更新
|
941次组卷
|
9卷引用:2014届高考数学总复习考点引领+技巧点拨第八章第3课时练习卷
(已下线)2014届高考数学总复习考点引领+技巧点拨第八章第3课时练习卷2017届江苏苏州市高三暑假自主学习测试数学试卷云南省南涧彝族自治县民族中学2017-2018学年高二9月月考数学(文)试题甘肃省武威第十八中学2017-2018学年高二下学期第二次月考数学(文)试题甘肃省武威第十八中学2018-2019学年高一上学期期末考试数学试题海南省海南枫叶国际学校2019-2020学年高二上学期期中数学试题河南省扶沟县第二高级中学2021-2022学年高一上学期第二次考试数学试题云南省昆明市官渡区第一中学2021--2022学年高一6月月考数学试题福建省将乐县第一中学2022-2023学年高一下学期第三次月考数学试题
名校
2 . 如图,在四棱锥
中,底面
为平行四边形,
为等边三角形,平面
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/87c3b3c3-5c46-46c5-a4bf-acaf7f75bf69.png?resizew=221)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正切值.
![](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/177678001b2ccde1db8f57fa5e017002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44f4120c94cb7176dc31fcac387b32e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/87c3b3c3-5c46-46c5-a4bf-acaf7f75bf69.png?resizew=221)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
2020-11-14更新
|
687次组卷
|
3卷引用:安徽省六安市第一中学2020-2021学年高二上学期第一次段考数学(文)试题
安徽省六安市第一中学2020-2021学年高二上学期第一次段考数学(文)试题(已下线)考点31 直线、平面垂直的判定及其性质-备战2021年高考数学(文)一轮复习考点一遍过河南省许昌市2021-2022学年高一下学期期末数学理科试题
解题方法
3 . 如图,在五面体
中,四边形
为矩形,
为等边三角形,且平面
平面
,
.
![](https://img.xkw.com/dksih/QBM/2020/7/20/2510137436266496/2511289076129792/STEM/f61cf4b9a68c4813baf6de61210f96e7.png?resizew=292)
(1)证明:平面
平面
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf84ed033bd035c2fe7552badd5e447d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1affed1ad8e53a73308c85849a72444.png)
![](https://img.xkw.com/dksih/QBM/2020/7/20/2510137436266496/2511289076129792/STEM/f61cf4b9a68c4813baf6de61210f96e7.png?resizew=292)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf84ed033bd035c2fe7552badd5e447d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5113ac6e656002f2d110f08ed753e9e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de7cb1d10dd759c0ebd487e4ca34ac8.png)
您最近一年使用:0次
4 . 如图,在三棱锥
中,
为正三角形,
为棱
的中点,
,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/1b56568e-cd28-4065-a671-4ca3b7e6e511.png?resizew=141)
(1)求证:
平面
;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ab13ef156d034b710d811e09b0be34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002471e69d992c4d10c8255ba152e7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/1b56568e-cd28-4065-a671-4ca3b7e6e511.png?resizew=141)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e351795b12a190463b86d3cd9c84a823.png)
您最近一年使用:0次
2019-11-05更新
|
1493次组卷
|
6卷引用:河南省洛阳市2019-2020学年高三上学期期中数学(文)试题
5 . 如图,在四棱锥
中,底面
是矩形,平面
平面
,
为
的中点,
,
,
.
![](https://img.xkw.com/dksih/QBM/2020/7/13/2505212234924032/2505949854744576/STEM/c2b845f230094ea7a35cd8e89b525e5d.png?resizew=266)
(1)证明:平面
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448cbac9a1ef3de7538a6b30cdc39582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b5e290c6b2c5508a3bf6117afbf7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b9da7aacb5c0b1ea1953490ef970c61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46711f8e26bd417c2cc948884f5271f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://img.xkw.com/dksih/QBM/2020/7/13/2505212234924032/2505949854744576/STEM/c2b845f230094ea7a35cd8e89b525e5d.png?resizew=266)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/393a753b57da192086a617f26ec89aea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f9217815bc1ffd116a48c0e418c24aa.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ffc61fd8724ba984fe0c4c3600d9c9.png)
您最近一年使用:0次
2020-07-14更新
|
300次组卷
|
2卷引用:河南省2020届高三6月大联考数学文科试题
6 . 如图,在三棱锥
中,平面
平面
,
为等边三角形,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/627c9f78-50d5-4614-8999-2f048297f810.png?resizew=198)
(1)证明:
;
(2)若
,求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/627c9f78-50d5-4614-8999-2f048297f810.png?resizew=198)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4cd8ba7eb52e38857830162e770f534.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2019-11-21更新
|
2832次组卷
|
11卷引用:2020届河南省南阳市第一中学高三上学期期终考前模拟数学(文)试题
2020届河南省南阳市第一中学高三上学期期终考前模拟数学(文)试题2019年11月四川省攀枝花市一模数学(文)试题四川省泸州市泸县第五中学2019-2020学年高三上学期期末考试数学(文)试题2020届四川省攀枝花市高三第一次统一考试文数试题安徽省阜阳市太和第一中学2020-2021学年高二(普通班)上学期期中数学试题安徽省阜阳市太和第一中学2020-2021学年高二(奥赛班)上学期期中数学试题四川省泸州市泸州老窖天府中学2020-2021学年高二上学期期中数学(文)试题宁夏吴忠中学2022届高三第二次月考数学(文)试题四川省宜宾市叙州区第一中学校2022-2023学年高二上学期第一学月考试数学(文)试题四川省泸县第四中学2022-2023学年高二上学期期中考试数学(文)试题浙江省嘉兴高级中学2023-2024学年高二上学期第一次教学调研数学试题
7 . 如图,
垂直于
所在的平面
,
为
的直径,
是弧
上的一个动点(不与端点
重合),
为
上一点,且
是线段
上的一个动点(不与端点
重合).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/8527de37-362c-49e8-81ef-1b5165b87c63.png?resizew=135)
(1)求证:
平面
;
(2)若
是弧
的中点,
是锐角,且三棱锥
的体积为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bc4cd549d91b4cc0b87aff3315d2a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb398137779190b35492d9f06d5fbc3.png)
![](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/90bcd6fd53460c1f987560772f13cda1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/8527de37-362c-49e8-81ef-1b5165b87c63.png?resizew=135)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843adec8fba1741ccb81a9017cfb815f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c37adec1fdcedfcf2d9e1bab990b89f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d55e3246d62e3016412a26a3ae5ba483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82168142f1873e3efe526b9efdbf4816.png)
您最近一年使用:0次
2019-06-02更新
|
756次组卷
|
4卷引用:【校级联考】河南省名校2018-2019学年高二5月联考数学(文科)试题
8 . 如图,在四棱锥
中,四边形
是边长为8的菱形,
,
是等边三角形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/0712d7b3-6aeb-4a14-9804-ca095273ae0d.png?resizew=178)
(Ⅰ)求证:
;
(Ⅱ)求四棱锥
的体积.
![](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/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e2a5a8708c06d509c766863a4d6279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89896cd1bf5bbabd2a350a0e8cee7c2c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/0712d7b3-6aeb-4a14-9804-ca095273ae0d.png?resizew=178)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5d56d8170b764b80a672cd6c861921.png)
(Ⅱ)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
9 . 如图,几何体EF-ABCD中,四边形CDEF是正方形,四边形ABCD为直角梯形,AB∥CD,AD⊥DC,△ACB是腰长为2
的等腰直角三角形,平面CDEF⊥平面ABCD.
(1)求证:BC⊥AF;
(2)求几何体EF-ABCD的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e051d14fd6a787387995331f5e6d026.png)
(1)求证:BC⊥AF;
(2)求几何体EF-ABCD的体积.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/011f6c09-0467-41c5-8ac5-536878a529c8.png?resizew=162)
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2019-01-17更新
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578次组卷
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2卷引用:【市级联考】河南省三门峡市2017-2018学年高一上学期期末考试数学试题
10 . 如图,三角形PCD所在的平面与等腰梯形ABCD所在的平面垂直,AB=AD=
CD,AB∥CD,CP⊥CD,M为PD的中点.
(1)求证:AM∥平面PBC;
(2)求证:BD⊥平面PBC.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求证:AM∥平面PBC;
(2)求证:BD⊥平面PBC.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/18318b17-d245-47df-85d6-a3c46e131de6.png?resizew=188)
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2019-03-26更新
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1725次组卷
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3卷引用:【全国百强校】江苏省扬州中学2019届高三下学期3月月考数学试题