题目

在如图所示的几何体中，四边形ABCD为正方形，平面ABCD，，，． Ⅰ求证：平面PAD； Ⅱ求PD与平面PCE所成角的正弦值； Ⅲ在棱AB上是否存在一点F，使得平面平面PCE？如果存在，求的值；如果不存在，说明理由． 答案：When was the last time someone unexpectedly did something nice for you? Not someone you knew, but a total stranger? It’s happened to me a few times, but two instances really stand out.A few years ago, I was dining in a restaurant with a friend who kept talking about himself, completely not aware of the fact that I was sitting there in misery. It wasn’t my friend’s talks that made me suffer. I was recovering from a broken heart, and just sitting down to dinner reminded me of my last relationship. I could have burst into tears right there at the table.When we picked up the check, the waitress said, “Your meal was already paid for.” My friend and I didn’t have a clue how it happened. Then I remembered a man I saw out of the corner of my eye. He was dressed in mostly white, sat down at the bar, had a beer, and stayed for maybe ten minutes. The waitress said, “Yes, the gentleman in white paid for you.” It felt like an angel was saying, “I see you, honey. It’s going to be okay.”Just last year, I was running a half?marathon. With just 1 mile to go, I was out of gas. Runners call it “hitting the wall”. I thought I couldn’t move another inch. Out of nowhere, a stranger came up to me and said, “What’s your name, sweetie? Jennifer? Okay, Jennifer, let’s go! Come on! It’s just around the corner! You can do it!” And he ran with me until I picked up my pace. I found him at the finish line to thank him for the encouragement only to learn he wasn’t even supposed to be in the race that day.I still shake my head when I think of these momentary angels that came to me at my point of need. Do you have any experiences like these?1.Which of the following is the best title for the passage?A．The kindness of strangersB．Valuable friendshipC．Two special experiencesD．Helping others is worthwhile2.According to the passage, the man in white ________.A．was the author’s friendB．had a big meal in the restaurantC．was generous and kind?heartedD．enjoyed making fun of others3.The underlined expression in the passage means “________”．A．being hurt by the wall B．winning the gameC．taking a deep breath D．running out of energy4.Who is the stranger in the marathon race?A. the writer’s friendB. the winner of the raceC. an athlete in the race D. a stranger passing by