题干

如图:在四棱锥P﹣ABCD中,底面ABCD是菱形,∠ABC=60°,PA⊥平面ABCD,点M,N分别为BC,PA的中点,且PA=AB=2.

(Ⅰ)证明:BC⊥平面AMN;

(Ⅱ)求三棱锥N﹣AMC的体积;

(Ⅲ)在线段PD上是否存在一点E,使得NM∥平面ACE;若存在,求出PE的长;若不存在,说明理由.


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解:(Ⅰ)证明:∵ABCD为菱形,

∴AB=BC

又∠ABC=60°,

∴AB=BC=AC,

又M为BC中点,∴BC⊥AM

而PA⊥平面ABCD,BC⊂平面ABCD,∴PA⊥BC

又PA∩AM=A,∴BC⊥平面AMN

(II)∵ SA

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    Many times we tend to use our hands to explain our needs and thoughts.____So you must be cautious when using hand gestures in communication.

    Hand gestures are a way of communicating with others and conveying your feelings. These gestures are most helpful when one is speaking to someone with no language in common. The meanings of hand gestures in different cultures may translate into different things.____Former President George W. Bush had to face a major faux pas(失礼) during a visit to Australia. He tried to signal a peace sign by waving the two-finger or V-sign at the crowd.

    You may think of this as a simple gesture, but he committed a major error.____The meaning of this hand gesture in Australia was asking the crowd to screw themselves, a rude expression used to show you're very angry!____Therefore, it is very important to understand the meanings of gestures before you travel to different countries.

    ____Those considered as good gestures in one country may be termed as offensive gestures in some countries. So, if you are a frequent flier to different countries, improve your communication skills by learning the meaning of hand gestures.

A. Here is a very common example.

B. Instead of his palm facing outwards, it faced inwards.

C. The great man received warm welcome by the Australians.

D. We communicate not only by words, but by hand gestures as well.

E. A serious error committed by the then most powerful man in the world.

F. But the same hand gesture may mean something quite offensive to a person from a different cultural background.

G. Before you communicate with people in different cultures, you need to understand the meaning of gestures.