题目

在四棱锥中，底面四边形为直角梯形，侧面为等边三角形，、分别为、的中点，平面，，，，．（1）求证：平面，（2）求异面直线与所成角的余弦值；（3）求到平面的距离． 答案：【答案】（1）证明见解析；（2）；（3）.【解析】（1）取的中点，连接、，证明出四边形为平行四边形，进而可得出，利用线面平行的判定定理可证得结论成立；（2）取的中点，连接，可得出，然后以点为坐标原点，、、所在直线分别为、、轴建立空间直角坐标系，写出、的坐标，利用空间向量法可 第三部分：阅读理解（共20小题，每题2分，满分40分） 阅读下列短文，从每题所给的四个选项（A、B、C和D）中，选出最佳选项,并在答题卡上将该项涂黑。 I was walking along Orchard Road when I realized a tall young man wearing a jacket and tie was following me. I noticed him because not many people wear a jacket and tie in the middle of a hot summer day, and I had already seen this man four times that afternoon. To make sure he was following me, I walked on quickly, turned right into a shopping center and then stopped to look in a shop window. Soon the man appeared and stopped at another shop window. I walked on and stopped several times. When I stopped, he stopped too. I began to be rather worried and decided to try to get rid of this strange man. When I saw a taxi coming, I jumped into it. As I was telling the taxi driver where to go, I found the man get into another taxi, which then followed mine. As the two taxies slowly made their way along Orchard Road, I looked back at the taxi behind, and saw that the stranger was looking out at me. At MRT station, I told the taxi driver to stop and I got out. As I was paying my fare, I saw the man was getting out of his taxi. By now I got angry, so I turned and walked straight to him. I asked him why he was following me. At first he said he was not following me at all, but when I threatened (威胁) to call the police, he admitted he was. He then told me that he was a journalist (news reporter) and that he was writing an article on how elderly people in Singapore spend their time. He said he was observing me to gather materials for his article. 56. What is strange about the man who followed the writer? A. He seemed to be wearing too much. B. He was out on such a hot day. C. He walked quickly behind.       D. He was a tall young man. 57. Why did the writer get into a taxi? A. To test the young man.                   B. To call the police. C. To lose the young man.                  D. To get home earlier. 58. What did the stranger do when the writer jumped into a taxi? A. He tried to stop the taxi. B. He got into another taxi. C. He almost gave up following him. D. He made his way along Orchard Road. 59. The stranger followed the writer because ______. A. he was interested in elderly people B. he often did such things C. he was writing a book about old people D. he needed materials for his article