题目

如图，四棱锥中，底面是平行四边形，，，平面．（1）证明：平面；（2）求直线与平面所成角的正弦值． 答案：【答案】（1）证明见解析；（2）．【解析】（1）根据菱形对角线互相垂直及平面ABCD，由线面垂直的判定定理得到平面PBD；（2）可直接作出线面角用几何法求之，也可建立空间直角坐标系用向量法求之．（Ⅰ）底面ABCD是平行四边形且，是菱形，即，又平面ABCD，得，所以平面PBD．（Ⅱ）方法一（几何法词汇检测【1】The price of houses _______(上升)a lot in Changshu last year, but it dropped a little this year.【2】I can see the things far away _______(清晰)with the help of the binoculars.【3】The radio says it will be much _______(雾)tomorrow morning.【4】Don`t take the bag away. It is one of the _______(登山者).【5】The man is happily _______(描述)what he saw during his stay in France.【6】James s______ much time in cooking every day.【7】一Sandy，you look very n______ .一Yes. This is my first time to introduce myself in front of so many people.【8】一What are the students talking about?一They are ______ where to go on their school trip.【9】一How much information did you find about this painter?一Oh，I tried, but I found ______ .【10】一Would Aimee get lost when she travels alone in such a big city?一Don't worry. She has a very good sense of ______ .