(1)解:∵ABCD是正方形,
∴AC⊥BD,OA=OB,
∴∠AOF=∠BOE=90°,
∵AG⊥BE,
∴∠FGB=90°,
∴∠OBE+∠BFG=90°,∠FAO+∠AFO=90°,
∵∠AFO=∠BFG,
∴∠FAO=∠EBO,
∵在△AFO和△BEO中
∴△AFO≌△BEO(ASA),
∴OE=OF.
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/e4dde71190ef76c60a70159a9e16fdfaae5167e5?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
(2)解:∵四边形ABCD是正方形,
∴∠ACB=∠DAC=45°,∠ABE+∠EBC=90°,
∵EH⊥BE,
∴∠AEH+∠AEB=90°,
∵AE=AB,
∴∠ABE=∠AEB,
∴∠CBE=∠AEH,
∵AE=AB=BC,
∵在△BCE和△EAH中
∴△BCE≌△EAH(ASA),
∴CE=AH,
∵AB=BC=1,
∴AC=
,
∵AE=AB=1,
∴AH=CE=AC-AE=
-1.