题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042846-16741.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042846-38234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042846-12612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042847-62646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042847-14176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042847-54870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042847-43798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042847-17190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042848-37719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042848-45537.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042848-49166.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042846-12612.png)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042848-15781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042848-26497.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042849-10856.png)
解析
试题分析:(Ⅰ)证法一是取
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042848-15781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042849-71811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042849-53836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042849-53836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042849-74267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042849-53060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042850-94230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042850-42058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042850-29695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042850-18178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042850-13665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042850-94230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042849-53060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042850-94230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042851-23019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042851-14580.png)
试题解析:解法一:(Ⅰ)取
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042848-15781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042849-71811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042851-34763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042851-93680.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042852-50395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042852-58443.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042852-61498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042852-93573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042852-65184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042853-89733.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042853-96186.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042853-27831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042846-12612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042853-93909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042846-12612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042848-49166.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042846-12612.png)
(Ⅱ)依题得,以点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042853-51056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042853-61629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042854-11099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042854-78776.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042854-97166.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042854-50266.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042854-84558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042855-23664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042855-51122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042855-56369.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042855-67500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042855-25390.png)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042848-26497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042856-99430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042856-61730.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042856-57449.png)
取
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042856-29126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042856-69909.png)
又设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042848-15781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042848-26497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042856-61114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042857-42145.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042857-74490.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042848-15781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042848-26497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042849-10856.png)
解法二:(Ⅰ)取
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042857-85878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042850-29695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042857-35826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042858-24885.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042858-44321.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042858-87325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042846-12612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042858-18459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042846-12612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042858-99506.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042846-12612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042859-77059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042846-12612.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042859-14646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042846-12612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042859-27337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042846-12612.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042859-70968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042859-55703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042846-12612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042900-78967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042846-12612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042848-49166.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042846-12612.png)
(Ⅱ)同解法一. 13分
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042822-27812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042822-94267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042823-54054.png)
(I)若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042823-95258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042823-19895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042823-87794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042824-26362.png)
(II)若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042823-95258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042823-19895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042824-74516.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042824-66788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042823-95258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042811-50300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042811-98636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042811-23133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042757-34446.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042757-43040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042758-75315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042758-53110.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042758-13687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042758-37260.png)
(I)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042759-22998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042759-60334.png)
(II)求
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042759-62825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042759-40912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022042759-33580.png)
A.若分别作△BAD和△CAD的边AD上的高,则这两条高所在直线异面
B.若分别作△BAD和△CAD的边AD上的高,则这两条高长度相等
C.AB=AC且DB=DC
D.∠DAB=∠DAC
(Ⅰ)求几何体ABCDFE的体积;
(Ⅱ)证明:平面ADE∥平面BCF;
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