题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043204-92391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043204-88670.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043204-36644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043204-93611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043204-69211.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043204-46334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043204-43157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043204-85321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043204-38015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-26033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-74314.png)
(1)求四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043204-92391.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-94091.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-33450.png)
(3)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043204-85321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-33450.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-19170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-22848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-66727.png)
(2)证得
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043206-90443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043206-97943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043206-90443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043206-19851.png)
由四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043206-77892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-72960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-51539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-72960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-52353.png)
(3)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-26177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-52353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-45010.png)
解析
试题分析:(1)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043208-73233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043208-81174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043208-71756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043208-81174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043208-70046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043208-81174.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043208-73233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043209-77176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043208-73233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043206-90443.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043209-94461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043208-73233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043209-62437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-22848.png)
∴侧棱
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-19170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-22848.png)
在四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043209-65847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-19170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-22848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-22848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043209-31106.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043210-56049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043206-90443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043206-97943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043206-90443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043206-19851.png)
所以,四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043204-92391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043210-35058.png)
(2)在四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043209-65847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-19170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-22848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-22848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043209-31106.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043210-56049.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043206-90443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043206-97943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043206-90443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043206-19851.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043210-67441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043206-90443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043210-67441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043210-89207.png)
∴四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043206-77892.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-72960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-51539.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043211-20379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043211-95456.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-72960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-52353.png)
(3)∵侧棱
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-19170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-22848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043211-15240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043205-22848.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043211-84694.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043208-73233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043206-97943.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043208-73233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043209-77176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-52353.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043211-89547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043212-38691.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043212-93865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-26177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-52353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043212-12395.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043212-95419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-26177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-52353.png)
∵在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043213-84308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043209-31106.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043213-10339.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043213-15270.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043213-62201.png)
∴ 直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-26177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-52353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043207-45010.png)
考点:平行关系,垂直关系,体积与角的计算。
点评:中档题,立体几何问题中,平行关系、垂直关系,角、距离、面积、体积等的计算,是常见题型,基本思路是将空间问题转化成为平面问题,利用平面几何知识加以解决。要注意遵循“一作,二证,三计算”。利用“向量法”,通过建立空间直角坐标系,往往能简化解题过程。
核心考点
试题【如图,在四棱锥中,底面是直角梯形,∥,,⊥平面SAD,点是的中点,且,. (1)求四棱锥的体积;(2)求证:∥平面;(3)求直线和平面所成的角的正弦值.】;主要考察你对线线角等知识点的理解。[详细]
举一反三
A.直线与平面没有公共点 | B.直线与平面相交 |
C.直线与平面平行 | D.直线与平面最多只有一个公共点 |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043147-30600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043147-74019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043148-20373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043148-95618.png)
A.![]() ![]() |
B.![]() |
C.![]() |
D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043137-12740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043137-28500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043137-90159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043137-32396.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043138-19232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043138-32252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043138-12435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043138-39605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043138-32252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043139-17936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043138-32252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043139-49668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043138-32252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043139-22992.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043138-32252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043139-17450.png)
其中正确命题的序号是 (把你认为正确命题的序号都填上).
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043139-42699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043132-74913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043133-13525.png)
A.若![]() ![]() ![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043127-10662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022043127-69092.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
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