如图,在△ABC,BD⊥AC垂足为点D,CE⊥AB垂足为点E,延长CE到G,使CG=AB,若∠BCE=45°,求证F、G关于AB对称

Question

如图,在△ABC,BD⊥AC垂足为点D,CE⊥AB垂足为点E,延长CE到G,使CG=AB,若∠BCE=45°,求证F、G关于AB对称

Answer 1

连结AF,延长AF交BC于H,则AH⊥BC∵∠BCE=45º,∴∠ABC=∠BAH=∠BCE=45º,BE=CE∵AB=CG===>AB-BE=CG-CE===>AE=GE===>∠G=∠GAE=45º∵∠ABD+∠BAC=∠ACE+∠BAC=90º===>∠ABD=∠ACE∴△ABF≌△GCA===>...