题目

如图，在以为顶点的多面体中， 平面， 平面， ． （1）请在图中作出平面，使得，且，并说明理由； （2）求直线和平面所成角的正弦值． 答案：【解析】（1）如图，取中点，连接，则平面即为所求的平面. 显然，以下只需证明平面； ∵，∴且， ∴四边形为平行四边形，∴. 又平面， 平面， ∴平面. ∵平面， 平面，∴. 又平面， 平面， ∴平面， 又平面平面， ∴平面平面. 又平面， ∴平面，即平面.        6分 （2）过点作并交于， ∵平请阅读下面对话，根据对话内容从方框中选择恰当的句子填入空白中，使对话通顺、合理，意思完整。[Zhang Ji is chatting with his e-pal Tim on QQ.]T: Hi, how is it going these days?Z: Pretty good! We celebrated our Dragon Boat Festival last week.T: Dragon Boat Festival?【1】Z: To remember an ancient Chinese poet. T: 【2】Z: We usually eat rice dumplings on that day. But this year, we did something more interesting.T: What did you do?Z: Our school had a dragon boat race.T: 【3】 Who won the race?Z: Our class.T: 【4】Z: Thanks a lot. I hope you can come to China sometime.T: I hope so. 【5】Tell me more about them next time.Z: OK, I will. See you.T: See you!A. How do you usually celebrate it?B. We had a good time.C. What do you celebrate it for?D. Sounds interesting !E. I'm interested in Chinese traditions.F. Congratulations !G. Where did you have the race?