题目

（本小题满分14分）在如图所示的一张矩形纸片（）中，将纸片折叠一次，使点与重合，再展开，折痕交边于，交边于，分别连结和．1.（1）求证：四边形是菱形；2.（2）过作交于，求证：3.（3）若，的面积为，求的周长；  答案： 1.（1）连结交于，························ 1分当顶点与重合时，折痕垂直平分，················· 1分，····················· 2分在矩形中，，，···························· 3分．···························· 3分································ 4分四边形是菱形．2.（2）证明：过作交于，由作法，，··························· 5分由（1）知：，又，，···························· 6分，则······················· 7分 四边形是菱形，，．········· 8分3.（3）四边形是菱形，．······························ 9分设，，，······························· 10分      ①························ 11分又，则．    ②················ 12分由①、②得：························· 13分，（不合题意舍去）················ 14分的周长为·················· 14分     解析:略 

查看本题答案和解析