题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054126-52885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054126-63114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054126-80294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054127-42061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054127-54093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054127-22007.jpg)
(1)证明:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054127-89574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054128-77379.png)
(2)设AB,PA,BC的中点依次为M、N、T,求证:PB∥平面MNT
(3)求异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054128-41451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054128-26471.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054128-13988.jpg)
(1)证明:先得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054129-41707.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054127-42061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054129-14389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054129-35798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054129-69654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054127-89574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054128-77379.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054129-53457.png)
解析
试题分析:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054130-47749.jpg)
(1)证明:∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054126-63114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054126-80294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054129-41707.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054127-42061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054130-80892.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054129-14389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054130-87898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054130-65125.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054129-35798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054129-69654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054127-89574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054128-77379.png)
(2)连接MN,MT,NT; ∵M、N分别为AB、AP中点 ∴MN//PB
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054131-16705.png)
解:∵AB中点M,AP中点N,BC中点T,,则MN//PB,MT//AC
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054131-10220.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054131-75804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054131-38867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054131-94440.png)
在RT△ADC中,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054132-87427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054132-23305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054132-22205.png)
在RT△NAT中,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054132-77004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054133-96503.png)
故异面直线AC与PB所成的角的余弦值为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054129-53457.png)
点评:典型题,立体几何题,是高考必考内容,往往涉及垂直关系、平行关系、角、距离的计算。在计算问题中,有“几何法”和“向量法”。利用几何法,要遵循“一作、二证、三计算”的步骤,利用向量则能简化证明过程。本题属于立体几何中的基本问题。
核心考点
试题【如图,在四棱锥中,底面ABCD是一直角梯形,,,,且PA=AD=DC=AB=1.(1)证明:平面平面(2)设AB,PA,BC的中点依次为M、N、T,求证:PB∥】;主要考察你对线线角等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054111-96057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054111-74407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054111-41247.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054111-41947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054112-43022.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054112-39782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054112-39237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054112-80162.jpg)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054113-12310.png)
(2)若二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054113-18408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054113-73987.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054103-10124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054104-45528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054104-16161.png)
⑴ 求证:AC⊥SB;
⑵ 求二面角N—CM—B的正切值;
⑶ 求点B到平面CMN的距离。
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054057-79159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054057-77663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054057-25832.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054058-19307.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
如图1,在等腰梯形
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054040-21013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054040-18636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054041-22720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054041-52584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054041-28007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054041-58410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054041-13557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054042-17551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054040-21013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054042-65597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054042-17242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054042-84061.jpg)
(Ⅰ)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054042-52032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054043-54570.png)
(Ⅱ)设点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054043-57492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054043-80512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054043-57078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054044-48840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054044-84364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054044-37570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054044-16968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054044-57035.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054044-48840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054045-70126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054035-64966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054036-22948.png)
①
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054036-17226.png)
②
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054036-98972.png)
③
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054036-49143.png)
④若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022054036-69870.png)
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