斜三棱柱ABC﹣A1B1C1的各棱长为a，侧棱与底面所成的角为60°，且侧面ABB1A1垂直于底面．（Ⅰ）判断B1C与AC1是否垂直，并证明你的结论；（Ⅱ）求三棱柱的全面积．_刷题宝

题干

斜三棱柱ABC﹣A₁B₁C₁的各棱长为a，侧棱与底面所成的角为60°，且侧面ABB₁A₁垂直于底面．

（Ⅰ）判断B₁C与AC₁是否垂直，并证明你的结论；

（Ⅱ）求三棱柱的全面积．

上一题下一题 0.0难度选择题更新时间:2019-02-14 09:10:33

答案(点此获取答案解析）

解：（Ⅰ）B₁C与AC₁垂直．

证明如下：

连接BC₁，由题意知B₁C⊥BC₁

作B₁D⊥AB，由条件知B₁D⊥面ABC，

又侧棱与底面所成的角为60°，

∴D为AB的中点，

∴CD⊥AB，CD为CB₁在底面ABC上的射影

又B₁C

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