题目

如图，在直三棱柱ABC－A1B1C1中，已知AC⊥BC，BC＝CC1，设AB1的中点为D，B1C∩BC1＝E.求证：(1)DE∥平面AA1C1C；(2)BC1⊥AB1. 答案：【答案】(1)详见解析;(2)详见解析.【解析】试题分析:(1) 由题意知，E为B1C的中点，又D为AB1的中点，因此DE∥AC,根据线面平行的判定定理得证;(2)由CC1⊥平面ABC,可得AC⊥CC1，又因为AC⊥BC，由线面垂直的判定定理可得AC⊥平面BCC1B1，进而可得B1C⊥AC,又BC1⊥B1C,证得BC1⊥平面B1AC,故命题成立.试题解析:(1)由题意知Each nation has many volunteers(志愿者) who help to take care of others. They      books to the people in hospitals or homes for the aged. Sometimes they just visit them and play games with them or listen to their    .Other young volunteers go and work in the homes of people who are sick or     . They paint, clean up,      their houses or do their shopping.For boys who no longer have    , there is an organization called Big Brothers. College students and other men take these boys to baseball games or fishing places and help them to get to know things that boys      learn from their fathers.Each city has a number of clubs     boys and girls can go to play games or learn crafts (工艺). Some of these clubs organize short trips to the mountains, beaches, or other places of interest     . Most of these clubs use high school and college students as volunteers because they are young enough to      the names of boys and girls.Volunteers believe that the happiest people in the world are those who help to     i happiness to others.小题1:A．sellB．readC．throwD．show小题2:A．voicesB．speechesC．songsD．problems小题3:A．youngB．happyC．oldD．hungry小题4:A．polluteB．repairC．buildD．remove小题5:A．brothersB．sistersC．fathersD．mothers小题6:A．usuallyB．neverC．onlyD．seldom小题7:A．whichB．whoC．whenD．where小题8:A．nearbyB．farawayC．abroadD．home小题9:A．reportB．forgetC．rememberD．choose小题10:A．causeB．bringC．takeD．lend