2016年第二十七届“希望杯”全国数学邀请赛第2试,初二年级有这样一道试题:如图1,四边形ABDE和ACFG都是正方形,M是BC的中点,延长MA交EG于点H,求证:(1)AM=1/2EG;(2)AH⊥EG;(3)EG~2+BC~2=2(AB~2+AC~2).此题要求学生构造全等三角形、直角三角形来获得相关的线段和角的数量关系,考查直观想像、逻辑推理、数学运算等核心素养.此题图形是经典的(传统且典型),通常是先 In 2016 twenty-seventh “hope cup” national mathematics invitational game second test, the second grade have such a test: as shown in Figure 1, quadrilateral ABDE and ACFG are square, M is the midpoint of BC, to extend MA pay EG at point H, verify: (1) AM = 1 / 2EG; (2) AH ⊥ EG; (3) EG ~ 2 + BC ~ 2 = 2 (AB ~ 2 + AC ~ 2) Equal triangle, right triangle to get the number of lines and angles related to the number of examining visualization, logical reasoning, mathematical operations and other core literacy. The title of the graphic is classic (traditional and typical), usually the first