解题方法
1 . 如图,四棱锥
中,底面
为正方形,
底面
,
为
的中点.
平面
;
(2)求证:平面
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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.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/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa69a2247ad4d5231aa361349b12f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
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3卷引用:广西壮族自治区南宁市东盟中学2023-2024学年高二上学期开学考试数学试题
广西壮族自治区南宁市东盟中学2023-2024学年高二上学期开学考试数学试题陕西省西安市第六十六中学2022-2023学年高一下学期第二次月考数学试题(已下线)专题训练:线线、线面、面面平行与垂直证明大题-同步题型分类归纳讲与练(人教A版2019必修第二册)
2 . 请选择适当的方法证明下列结论:
(1)求证:
;
(2)已知
,求证:
.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c1d583e670dac4530bd57ac9118740.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e10cc5dd849caccce37fe98a26c598.png)
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4卷引用:广西百色市2021-2022学年高二下学期期末教学质量调研测试数学(文)试题
3 . 用综合法或分析法证明:
(1)如果
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd70f831f301205134280f6432c8f84d.png)
(2)求证
.
(1)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd70f831f301205134280f6432c8f84d.png)
(2)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7677985318eb222a2af0aef6e7dd28.png)
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名校
解题方法
4 . 如图四边形
是正方形,
平面
,
平面
,
,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/dd2be926-8b27-4cf4-aa03-27e00b88a67a.png?resizew=165)
(1)求证:平面
平面
;
(2)若点
为线段
中点.证明:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39967d6f3aed6ce7b6643787795d451d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb14af56d74a9d47d40cbbf844ebf63.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/dd2be926-8b27-4cf4-aa03-27e00b88a67a.png?resizew=165)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85091a82037ce6b2754ae98bd224763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb5255e2159617505e0c87d01437a57.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/855c45f898c4710ee3bf99bd9955029e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c54d01623f09f23103f03ba1135fc6a.png)
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2020-02-18更新
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2卷引用:广西梧州市藤县第七中学2021-2022学年高二上学期期中考试数学试题
5 . 用反证法证明命题“已知
为非零实数,且
,
,求证
中至少有两个为正数”时,要做的假设是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e7ef804eeb23618fbf91ead47587f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e80376a90437a9ef6049bbd389a4ff2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2018-06-07更新
|
734次组卷
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9卷引用:广西浦北中学2020-2021学年高二3月月考数学(文)试题
广西浦北中学2020-2021学年高二3月月考数学(文)试题【全国百强校】广东省中山市第一中学2017-2018学年高二下学期第二次段考数学(理)试题黑龙江省大庆市第十中学2017-2018学年高二下学期第二次月考数学(理)试卷【市级联考】湖南省张家界市2018-2019学年高二第一学期期末联考文科数学试题辽宁省沈阳市东北育才学校2018-2019学年高二下学期期中考试数学(文)试题辽宁省沈阳市重点高中协作校2018-2019学年高二下学期期中数学文科试题陕西省延安市吴起高级中学2019-2020学年高二下学期第一次质量检测数学(文)试题湖北省襄阳市2018-2019学年高二下学期期末数学(理)试题江西省上饶市横峰中学2019-2020学年高二下学期开学考试数学(文)试题
名校
6 . 已知△
中,
,求证
.
证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf7efa75e1f580910d41d954bc911cd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0caa3e6a0de075df4c9a869dfed4bf20.png)
画线部分是演绎推理的( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c0ad68bf0ca0d00461a269df127af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf7efa75e1f580910d41d954bc911cd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0caa3e6a0de075df4c9a869dfed4bf20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf1aa83a61bd003e09b68d51af984a4.png)
A.大前提 | B.三段论 | C.结论 | D.小前提 |
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2017-07-15更新
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3卷引用:广西陆川县中学2017-2018学年高二下学期开学考试数学(文)试题
名校
7 . 如图,直三棱柱
的所有棱长都是2,
分别是
的中点.
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98842968c75427c940b34de391a3a778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d06f8edd1a1f18ca2dae700c6a29ab4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/23/2b6a3e38-044b-4132-8316-b256242a0019.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
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10-11高二下·广西桂林·期中
名校
8 .
是正角形
所在平面外一点,
分别是
和
的中点,且
.
(1)求证:
是
和
的公垂线;
(2)求异面直线
和
之间的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/499f8f7f6f353710473da5ae3f1c8443.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/5/a8025d5c-d962-49f7-aad5-548c2fb7397d.png?resizew=140)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
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解题方法
9 . 在四棱锥
中,底面
为梯形,
,
,
,
,
,
⊥平面
.
(1)求证:平面
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9742a7f64ff91be02601331f4ef2bb4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28d6477c85c5a4ac410a884e92fbe53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b3539fcb35e07fcf3339eb04e7748d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee73452ee4d5437f1399f1235b95e55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab4007a35a23105744177d982caf747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb6823a329628699619a39cde927510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db37b5ce697dab3189a15881d00fcd0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28d6477c85c5a4ac410a884e92fbe53.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/16/a71e5192-9737-4ee3-9971-35af857f8eed.png?resizew=147)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a0d238b6e9b49bbea22a79402e8e4f.png)
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|
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4卷引用:广西平果市铝城中学2023-2024学年高二上学期期末模拟数学试题(二)
名校
10 . 如图,四棱锥
的底面
是平行四边形,
是边长为2的正三角形,平面
平面
为棱
的中点.
平面
.
(2)求直线
与平面
所成角的正弦值.
![](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/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df0ab48b6c32c1c594587bb86b39865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
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