如图，正三棱柱ABC﹣A1B1C1中，D是BC的中点，AA1=AB=1．（Ⅰ）求证：A1C∥平面AB1D；（Ⅱ）求二面角B﹣AB1﹣D的正切值；（Ⅲ）求点C到平面AB1D的距离．_刷题宝

题干

如图，正三棱柱ABC﹣A₁B₁C₁中，D是BC的中点，AA₁=AB=1．

（Ⅰ）求证：A₁C∥平面AB₁D；

（Ⅱ）求二面角B﹣AB₁﹣D的正切值；

（Ⅲ）求点C到平面AB₁D的距离．

上一题下一题 0.0难度选择题更新时间:2011-10-27 07:59:32

答案(点此获取答案解析）

证明：（Ⅰ）连结A₁B，AB₁，交于点E，则E是AB₁中点，连结DE，

∵D是BC的中点，

∴DE是△A₁BC的中位线，

∴DE∥A

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