1 . 如图1,在直角梯形
中,
,
,且
,现以
为一边向梯形外作正方形
,然后沿边
将正方形
翻折,使
,
为
的中点,如图2.
![](https://img.xkw.com/dksih/QBM/2021/6/16/2744371237044224/2803776941023232/STEM/73bc771f-6e4a-4584-b89a-4a6c489021ef.png?resizew=605)
(1)求证:
平面
;
(2)求证:平面
平面
;
(3)若
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0046177466c78f08d45449dc5639bf38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3da6e90f9c9617cd495abb57ab9b0e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://img.xkw.com/dksih/QBM/2021/6/16/2744371237044224/2803776941023232/STEM/73bc771f-6e4a-4584-b89a-4a6c489021ef.png?resizew=605)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac480d8d9d7821b62a603cf5cfda236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a814b70236a108be5d6e7ff271fe92.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c309e58bf083bad13abd549720a63a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82773737609e65dea3c5c67099f1b10d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a814b70236a108be5d6e7ff271fe92.png)
您最近一年使用:0次
2021-09-08更新
|
584次组卷
|
5卷引用:江西省兴国县将军中学2021-2022学年高二上学期月考数学(理)试题
名校
解题方法
2 . 在四棱锥P—ABCD中,平面PAB⊥平面ABCD,∠ABC=∠BCD=90°,PC=PD,PA=AB=BC=1,CD=2.
![](https://img.xkw.com/dksih/QBM/2021/12/22/2878188120391680/2917523442221056/STEM/fa3483a1-e42e-4020-99e1-f7c09afe43a2.png?resizew=185)
(1)证明:PA⊥平面ABCD;
(2)求点C到平面PBD的距离.
![](https://img.xkw.com/dksih/QBM/2021/12/22/2878188120391680/2917523442221056/STEM/fa3483a1-e42e-4020-99e1-f7c09afe43a2.png?resizew=185)
(1)证明:PA⊥平面ABCD;
(2)求点C到平面PBD的距离.
您最近一年使用:0次
2022-02-16更新
|
262次组卷
|
5卷引用:江西省安福中学2021-2022学年高二上学期第一次段考数学(理)试题
名校
解题方法
3 . 如图,四边形
为正方形,
,
,且
,
,延长
相交于点
,连接
,
平面
.
![](https://img.xkw.com/dksih/QBM/2021/9/28/2817907379585024/2821526296436736/STEM/3aabd719b0e8420ca9107259815edb09.png?resizew=261)
(1)求证:
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae4c5cfe83c44c72a2d40695d18b2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a64f0bc01c1dbf0b4b87763141d8059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b021a72721e6ac70349104f8bf4b08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901a7eda97d6a307db76c4fb196ba3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012434c2c590eb70714d7c24fd63eaaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c81e1db197be2e4b396000fbaa3129.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4d781525777c7b5284dffc70b2a28a.png)
![](https://img.xkw.com/dksih/QBM/2021/9/28/2817907379585024/2821526296436736/STEM/3aabd719b0e8420ca9107259815edb09.png?resizew=261)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cb8697622fb9d281cf44feb4adaf14a.png)
您最近一年使用:0次
10-11高三上·广东茂名·期中
名校
解题方法
4 . 如图,四面体
中,
、
分别是
、
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/fb30b1be-9b20-46fc-be02-fd044cc27f15.png?resizew=202)
(1)求证:
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65d5853c26657db448af610ac72cca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6559aabe16c2318687089e7cc498b98.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/fb30b1be-9b20-46fc-be02-fd044cc27f15.png?resizew=202)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce03b310edce42191f9fa75a1c909ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
您最近一年使用:0次
2021-09-10更新
|
531次组卷
|
14卷引用:江西省上高二中2022届高三上学期第二次月考数学(文)试题
江西省上高二中2022届高三上学期第二次月考数学(文)试题江西省新余市重点高中2022届高三上学期第二次月考 数学(文)试题福建省泉州市晋江市南侨中学2019-2020学年高二上学期11月月考数学试题天津市静海县第一中学2017-2018学年高二10月学生学业能力调研数学试题云南省楚雄天人中学2020-2021学年高二3月月考数学(文)试题(已下线)2011届广东省高州三中高三上学期期中考试数学卷(已下线)2011届江苏省南京金陵中学高三预测卷2数学2014-2015学年黑龙江哈尔滨师大附中高二上学期期末考试理科数学卷山西省朔州市怀仁县第一中学2018-2019学年高二下学期期末数学试题陕西省咸阳市永寿中学2020-2021学年高三上学期开学考试数学(文)试题(已下线)专题19 立体几何综合-2020年高考数学(文)母题题源解密(全国Ⅰ专版)吉林省东北师大附中、长春市十一高中、吉林一中、四平一中、松原实验中学2021-2022学年高三上学期联合模拟考试数学(文)试题黑龙江省大庆铁人中学2021-2022学年高三上学期期中考试文科数学试题上海市七宝中学2022届高三冲刺模拟卷二数学试题
解题方法
5 . 如图,在正三棱柱中ABC-A1B1C1,D为AB的中点.
![](https://img.xkw.com/dksih/QBM/2021/12/21/2877244010323968/2880285898661888/STEM/470d8d08bca14a2eb4f91c7971d4f12b.png?resizew=269)
(1)证明:BC1∥平面A1CD;
(2)已知AB=2,CC1=
,求点B1到平面A1CD的距离.
![](https://img.xkw.com/dksih/QBM/2021/12/21/2877244010323968/2880285898661888/STEM/470d8d08bca14a2eb4f91c7971d4f12b.png?resizew=269)
(1)证明:BC1∥平面A1CD;
(2)已知AB=2,CC1=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
您最近一年使用:0次
6 . 平行四边形ABCD中(图1),∠A=60°,AB=2AD,将△ABD以BD为折痕折起,使得平面
BD⊥平面BCD,如图2.
![](https://img.xkw.com/dksih/QBM/2021/9/24/2815032841920512/2815709350641664/STEM/f9630d573aba4d76b6c72c439bc47b3c.png?resizew=401)
(1)证明:平面
BC⊥平面
BD;
(2)已知AD=1,点M为线段
C的中点,求点C到平面MDB的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://img.xkw.com/dksih/QBM/2021/9/24/2815032841920512/2815709350641664/STEM/f9630d573aba4d76b6c72c439bc47b3c.png?resizew=401)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
(2)已知AD=1,点M为线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
您最近一年使用:0次
2021-09-25更新
|
497次组卷
|
3卷引用:江西省南昌市第十中学2021-2022学年高二下学期第一次月考数学(文)试题
7 . 如图,直三棱柱ABC-A1B1C1中,D是AB的中点,AC=BC=3,AB=3
,AA1=6.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/1f8bda60-8f93-42d1-85a9-d331f813abb5.png?resizew=139)
(1)求证:AC1//平面CDB1;
(2)求点C1到平面CDB1的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/1f8bda60-8f93-42d1-85a9-d331f813abb5.png?resizew=139)
(1)求证:AC1//平面CDB1;
(2)求点C1到平面CDB1的距离.
您最近一年使用:0次
2021-08-27更新
|
696次组卷
|
4卷引用:江西省智学联盟体(南昌市第二中学等)2022届高三上学期第一次联考数学(文)试题
江西省智学联盟体(南昌市第二中学等)2022届高三上学期第一次联考数学(文)试题(已下线)专题01 立体几何求体积-【解题思路培养】2022年高考数学一轮复习解答题拿分秘籍(全国通用版)(已下线)专题19 立体几何(解答题)-备战2022年高考数学(文)母题题源解密(全国甲卷)黑龙江省嫩江市第一中学等2021-2022学年高三上学期期末联考数学(文)试题
8 . 如图,在四棱锥O-ABCD中,底面ABCD是边长为1的正方形,OA⊥底面ABCD,OA=2,M为OA的中点,N为BC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/3581725f-017d-4aa0-ad4f-54c0b7ea69d9.png?resizew=164)
(1)证明:直线MN//平面OCD;
(2)求点B到平面OCD的距离.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/3581725f-017d-4aa0-ad4f-54c0b7ea69d9.png?resizew=164)
(1)证明:直线MN//平面OCD;
(2)求点B到平面OCD的距离.
您最近一年使用:0次
2021-11-20更新
|
371次组卷
|
2卷引用:江西省萍乡市芦溪中学2021-2022学年高二上学期第一次段考数学(理)试题
解题方法
9 . 如图,在直三棱柱
1中,AB⊥BC,
,BC=1,E,F分别是
,BC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/c4a22223-f736-4a59-88ac-f5fb268c0fab.png?resizew=154)
(1)求证:
平面ABE;
(2)求点A到平面BCE的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16cfb38323095090b0fe5eee70b24210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/c4a22223-f736-4a59-88ac-f5fb268c0fab.png?resizew=154)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0447e46f2d9b39960ae1f1294ed8a2f2.png)
(2)求点A到平面BCE的距离.
您最近一年使用:0次
2021-08-24更新
|
260次组卷
|
2卷引用:江西省宜春市丰城市第九中学2020-2021学年高二下学期第三次月考数学(理)试题
名校
解题方法
10 . 如图,在斜三棱柱
中,
是
的中点,
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/d0965977-06d8-472a-8070-c2e95c7690b8.png?resizew=224)
(1)求证:
⊥平面
;
(2)若
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e5981445b6f2a6c58974158d96a4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e89a358226b4be8786077a60555c69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ea8821d44ee1f9332096263e7508e9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/d0965977-06d8-472a-8070-c2e95c7690b8.png?resizew=224)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9ffc43a56921fe79f8602636b8b0f.png)
您最近一年使用:0次