笔者所在区的一次期末统考中,有一道难度较大的题目,特对此进行分析和思考,与同行们交流.一、原题呈现四边形ABCD为正方形,点E为射线AC上一点,连结DE,过点E作EF⊥DE,交射线BC于点F,以DE、EF为邻边作矩形DEFG,连结CG.(1)如图1,当点E在线段AC上时,①求证:矩形DEFG是正方形;②求证:AC=CE+CG.(2)如图2,当点E在线段AC的延长线上时,请你在图2中画出相应图形,并直接写出AC、CE、CG之间的数量关系. In the author's area of ​​a final exam, there is a more difficult topic, especially on this analysis and thinking, and colleagues exchange. First, the original quadrilateral ABCD showed square, point E for the ray AC point, the link DE , The point E for EF ⊥ DE, intersects the line BC at point F, DE, EF adjacent to the rectangle DEFG, link CG. (1) When the point E is on the line segment AC, (2) As shown in Figure 2, when point E is on the extension line of line segment AC, please draw the corresponding graphic in Figure 2 and write out the AC, CE , The relationship between the number of CG.