Question

如图，已知E、F分别为矩形ABCD的边BA、DC的延长线上的点，且AE＝AB，CF＝CD，连结EF分别交AD、BC于点G、H．请你找出图中与DG相等的线段，并加以证明．

Answer 1

图中与DG相等的线段为BH，即BH=DG               

证明：∵四边形ABCD是矩形

∴∠B=∠D,AB∥CD，AB=CD                        

 又∵AE=AB, CF=CD

∴AE=CF                                         

∴EB=FD                                        

∵AB∥CD

∴∠E=∠F                                                                                                            

在△EBH和△FDG中

∴△EBH≌△FDG                                  

∴BH=DG