解题方法
1 . 如图,直三棱柱
中,O是
与
的交点,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2021/11/4/2844051464593408/2844240677027840/STEM/f969361d0d5c4bf29f946fe3cd223048.png?resizew=228)
(1)证明:
平面
;
(2)若侧面
是正方形,
,求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/2021/11/4/2844051464593408/2844240677027840/STEM/f969361d0d5c4bf29f946fe3cd223048.png?resizew=228)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6748d9b9948485c5ba87ca8751c6e053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若侧面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ba5383e768dc86e1bfd79c10f96f4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99ef32b30524326ce26f117cd7f5a91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
您最近一年使用:0次
解题方法
2 . 如图,在四棱台
中,底面
为矩形,
,
,
,
.E为
靠近D点的三等分点,平面
与直线
交于点P,连接
交
于O点.
![](https://img.xkw.com/dksih/QBM/2021/2/2/2649276907134976/2650969003556864/STEM/86dbe61cbd3c494fa29fbe655d1438aa.png?resizew=382)
(1)求证:
;
(2)若F为
的三等分点(靠近B点),请在线段
上确定一点Q,使
平面
,并证明之.
![](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/077c956ac0eb05cf120e14f17413dfa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e05c4eff7615455af8500fa211b0b071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c02ffbf0d9a3a73b896732082710c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99644f0e0881bc7bf383a88eb92c0949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/2021/2/2/2649276907134976/2650969003556864/STEM/86dbe61cbd3c494fa29fbe655d1438aa.png?resizew=382)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d31767eb718a0327eca546fe6a189cb.png)
(2)若F为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a929faf549d8b8f1cd36d7a98257ace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc4124fd4832415701968dbec3e7499.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,在以
为顶点的五面体中,
为
的中点,
平面
,
∥
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2020/4/22/2446938607181824/2448272898809856/STEM/a069566f31f24770a2f0d0d38a2b7b43.png?resizew=225)
(1)试在线段
找一点
使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
平面
,并证明你的结论;
(2)求证:
平面
;
(3)求直线
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d75df9d80ce1e0b7cb50464e293864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cad7b03f934718b18ce34cdf0b85863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c14a66ed4bd66df65bc42c4ac1ed15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/922f76192990e3a69805209d58586987.png)
![](https://img.xkw.com/dksih/QBM/2020/4/22/2446938607181824/2448272898809856/STEM/a069566f31f24770a2f0d0d38a2b7b43.png?resizew=225)
(1)试在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
您最近一年使用:0次
4 . 如图,边长为4的正方形ABCD所在平面与正△PAD所在平面互相垂直,M,Q分别为PC,AD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/4e134e23-0c80-48ab-aa41-75b35e24e2c8.png?resizew=191)
(1)求证:PA//平面MBD.
(2)试问:在线段AB上是否存在一点N,使得平面PCN⊥平面PQB?若存在,试指出点N的位置,并证明你的结论;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/4e134e23-0c80-48ab-aa41-75b35e24e2c8.png?resizew=191)
(1)求证:PA//平面MBD.
(2)试问:在线段AB上是否存在一点N,使得平面PCN⊥平面PQB?若存在,试指出点N的位置,并证明你的结论;若不存在,请说明理由.
您最近一年使用:0次
名校
解题方法
5 . 如图,在菱形
中,
⊥平面
,且四边形
是平行四边形.
![](https://img.xkw.com/dksih/QBM/2017/10/11/1793058665390080/1795120232783872/STEM/af55a97e45d5478abe96891c2a29a524.png?resizew=212)
(1)求证:
;
(2)当点
在
的什么位置时,使得
∥平面
,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ab4fdfc612c9fa2dd8ae24904192d8.png)
![](https://img.xkw.com/dksih/QBM/2017/10/11/1793058665390080/1795120232783872/STEM/af55a97e45d5478abe96891c2a29a524.png?resizew=212)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf21399dcf3682bf5d3f9cbd5eed86c.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711da913d92fc989e581bcfdfe092a18.png)
您最近一年使用:0次
2017-10-14更新
|
686次组卷
|
3卷引用:浙江省嘉兴市第一中学2017-2018学年高二10月月考数学试题
6 . 如图,在直四棱柱
中,底面
为等腰梯形,
,
,
,
,
、
、
分别是棱
、
、
的中点.
![](https://img.xkw.com/dksih/QBM/2017/8/14/1751785702260736/1751921621311488/STEM/d073073543654760aa90c1b49c9b5e85.png?resizew=201)
(1)证明:直线
平面
;
(2)求证:面
面
.
![](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/49149989ccd8350bf530c7cb750f7014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ad8d16722f5b9e7fd2602f14d5ffbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.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/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/2017/8/14/1751785702260736/1751921621311488/STEM/d073073543654760aa90c1b49c9b5e85.png?resizew=201)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c792ca780d16af1621703504da48fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a456b9e47c1dc1ca65494bf60518994b.png)
(2)求证:面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878659443e9a71a7649f11a557369f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
您最近一年使用:0次
2017-08-14更新
|
330次组卷
|
2卷引用:浙江省宁波市余姚中学2017-2018学年高二(宜张班)上学期第一次质量检测数学试题
解题方法
7 . 如图,四棱锥
的底面是边长为
的正方形,侧棱
底面
,且
,
是侧棱
上的动点.
![](https://img.xkw.com/dksih/QBM/2017/10/21/1806565718491136/1807228388163584/STEM/c114c5abd9a243c2834a2cc99f0f6970.png?resizew=176)
(1)如果
是
的中点,求证
平面
.
(2)是否不论点
在侧棱
的任何位置,都有
?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.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/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://img.xkw.com/dksih/QBM/2017/10/21/1806565718491136/1807228388163584/STEM/c114c5abd9a243c2834a2cc99f0f6970.png?resizew=176)
(1)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93a5ea2c4dab70518bed4b3f2989f47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)是否不论点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509d8dd6031dc0ef92075877e53fe201.png)
您最近一年使用:0次
2017-10-31更新
|
299次组卷
|
2卷引用:浙江省台州市蓬街私立中学2019-2020学年高二上学期第一次月考数学试题
12-13高二上·浙江杭州·期中
解题方法
8 . 如图,直三棱柱
中,已知
,
,
是
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/9/1f651409-9fc2-4241-b792-5828526e8e09.png?resizew=181)
(1)求证:
平面
;
(2)当点
在
上什么位置时,会使得
平面
?并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e47739be8ea23755014d80b408e6a36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/9/1f651409-9fc2-4241-b792-5828526e8e09.png?resizew=181)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762b8cac66d86a013ba839266b023e54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bea124cef7ab3fd8069243e9894d1c59.png)
(2)当点
![](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/4560fa4ad459b58b723c74bd24e51ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431e8bf1a5f9ac9a2ec82c11f31a4afe.png)
您最近一年使用:0次
12-13高二上·浙江杭州·期中
解题方法
9 . 如图,在四棱锥
中,侧棱
,底面
是菱形,
与
交于
点.
(Ⅰ)求证:
平面
;
(Ⅱ)若
为
中点,点
在侧面
内及其边界上运动,并保持
,试指出动点
的轨迹,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37505861cb6bd5dd3c95da992510c3ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e8f350b865da747d0b90243fa1ce28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5000fea066102e62cf2128ccbbd2b3e3.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c009f663ad2b0c3ba521daf4b86b066f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc56fdf70e65bd88980c64af96b83da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/2012/1/2/1570671330615296/1570671336144896/STEM/95dc458d40bf401a9713ba69898dfadf.png?resizew=190)
您最近一年使用:0次
10 . 如图,四棱锥
中,底面
是正方形,
平面
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2018/5/5/1938553481633792/1940735921700864/STEM/53c9ec8cd2a7424b8c99ed8f8b79aa71.png?resizew=211)
(1)求证:
平面
;
(2)证明: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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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![](https://img.xkw.com/dksih/QBM/2018/5/5/1938553481633792/1940735921700864/STEM/53c9ec8cd2a7424b8c99ed8f8b79aa71.png?resizew=211)
(1)求证:
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(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
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您最近一年使用:0次
2016-12-04更新
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617次组卷
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7卷引用:2015-2016学年浙江金华等三市部分学校高二下学期期中数学试卷