题目

在三棱柱中，四边形是菱形，，，，，点M、N分别是、的中点，且.（1）求证：平面平面；（2）求四棱锥的体积. 答案：【答案】（1）证明见解析；（2）.【解析】（1）要证面面垂直需要先证明线面垂直，即证明出平面即可；（2）求出点A到平面的距离，然后根据棱锥的体积公式即可求出四棱锥的体积.（1）连接，由是平行四边形及N是的中点，得N也是的中点，因为点M是的中点，所以，因为，所以，又，，所以平面，又听下面一段材料，回答第1-4题。1. What disease did the woman's first husband die of?   A. Heart disease.    B. Yellow fever.C. Lung cancer.2. Which of the following is RIGHT? A. Madison and Todd raised her son together who she had with her first husband.B. Madison was not happy when he stayed with Todd.C. Madison and Todd had a son together.3. How many years did their marriage last?   A. Fifteen years.    B. Fourteen years.C. Forty-one years.4. Why didn't Madison's retirement last long? A. Because he became president in 1801.B. Because Jefferson appointed him as Secretary of State.C. Because he died in 1801.