题目

已知：如图①，②，在矩形ABCD中，AB=4，BC=8，P，Q分别是边BC，CD上的点．(1)如图①，若AP⊥PQ，BP=2，求CQ的长； (2)如图②，若=2，且E，F，G分别为AP，PQ，PC的中点，求四边形EPGF的面积． 答案：【答案】(1)CQ=3；(2)S四边形EPGF=4.【解析】（1）易证△ABP∽△PCQ，根据对应线段成比例即可求出CQ；（2）取BP的中点H，连结，由三角形的中位线的性质可得四边形是直角梯形，由=2，设CQ=a，则BP=2a，用含a的代数式表示出EH,FG,HP,HG，用梯形和三角形的面积公式求得的值即可.解：(1)由△ABP∽△PCQ．∴．(2)取BP 根据短文内容及首字母提示，填写所缺单词， 　　Chuck Wall teaches management and human relations at Bakersfield College．He walked into class one day and told his students that their h　　1　　 was to perform one act of random(任意的)kindness．His students did not understand the assignment(任务), but the professor would not answer their questions．He e　　2　　 his students to find it out for themselves． 　　One week later, the students entered the classroom excited to s　　3　　 their stories．One student told of distributing blankets to the homeless, another had contacted a long, lost friend, and another student r　　4　　 that he had helped a dog to find its owner．Students were energized(激励)by the homework assignment and wanted other people to be kind too．W　　5　　the support of local businesses, the students made stickers to put on cars that invited people to do something k　　6　　 for others．They sold the stickers and decided to donate the money to a center for the blind –not surprising as Professor Wall is blind．Since then, s　　7　　 kindness activities have been organized in schools all over the world．Many schools organize a Random Acts of Kindness Week, a　　8　　November 13, to celebrate World Kindness Day．Some schools use each day of Random Acts of Kindness Week to performd　　9　　 kind acts, such as making a new friend, helping someone, doing community service, or raising money for a charity．Students learn to c　　10　　other people and think about how small actions can make the world a better place．