题目

已知三棱锥P﹣ABC中，PA⊥平面ABC，AB⊥BC，D为PB中点，E为PC的中点， （1）求证：BC∥平面ADE； （2）求证：平面AED⊥平面PAB． 答案：【考点】直线与平面平行的判定；平面与平面垂直的判定． 【专题】证明题；空间位置关系与距离． 【分析】（1）由中位线定理和线面平行的判定定理，即可得证； （2）由线面垂直的性质和判定定理，以及通过面面垂直的判定定理，即可得证． 【解答】（1）证明：∵PE=EC，PD=DB，∴DE∥BC， ∵DE⊂平An artist goes to a beautiful part of the country for a holiday and stays with a farmer. Every day he goes out with his paints and brushes and paints until evening. When it gets dark he goes back to the farm and has a good dinner before he goes to bed. At the end of his holiday he wants to pay the farmer, but the farmer says, “No, I don’t want money. But give me one of your pictures. What’s money? In a week it will be finished, but your picture will still be there.” The artist is very happy and thanks the farmer for saying so about his pictures. The farmer smiles and answers, “It’s not that. I have a son in London. He wants to be an artist. When he comes home next month, I will show him your picture, and he will not want to be an artist any more, I think.” 54. Every day the artist _________ .  A. goes out to help the farmer           B. stays at the farmer’s home and eats a big dinner        C. paints pictures          D. works hard to get some money for the farmer 55. The artist thinks the farmer wants his picture because _______.  A. the farmer likes his drawing very much B. the farmer hates his pictures   C. the farmer wants to give it to his son D. the farmer wants to be an artist, too 56. What does the farmer mean in the last paragraph?  A. He likes the artist very much.  B. He would like his son to be an artist, too. C. He wants the artist to be his son’s teacher. D. He doesn’t like the artist’s paintings at all.