Question

AB=BC=CD=DA,过A,B,C,D分别作线段AH,BE,CF,DG,使H在DG上,E在AH上,F在BE上,G在CF

Answer 1

1、∵四边形ABCD是正方形∴AB＝AD＝BC＝CD∠A＝∠B＝∠C＝∠D在Rt△AEH和Rt△DHG中AH＝DGEH＝HG∴Rt△AEH≌Rt△DHG（HL）∴DH＝AE∠DEG＝∠AEH∵∠AEH＋∠AHE＝90°∴∠AHE＋∠DHG＝90°∴∠EHG＝90°2、∵DH＝AEvnrwAD＝AB∴AH＝BE∵EH＝EF∴Rt△AEH和Rt△BEF∴AE＝BF∠AEH＝∠BFE∵∠BEF＋∠BFE＝90°∴∠BEF＋∠AEH＝90°∴∠HEF＝90°3、∵AE＝BFaeAB＝BC∴BE＝CF＝DG∵CD＝BC∵CG＝BF∴Rt△BEF≌和Rt△CFG∴EF＝FG∠GFC＝∠BEF∵∠BEF＋∠BFE＝90°∴∠BFE＋∠GFC＝90°∴∠EFG＝90°4、在四边形EFGH中∠EHG＝∠HEF＝∠EFG＝90°EF＝EH＝HG＝FG∴四边形EFGH是正方形