Question

如图,在ABC的外侧,以AB,AC为边向外作正方形ABDE,ACFG

Answer 1

如图,⑴延长AM 到P使MP＝AM则AGPE是平行四边形.⊿ABC≌⊿EAP﹙SAS﹚

∠PAE＝∠ABC∠ABN+∠NAB＝∠PAE+∠NAB＝180º-90º＝90º∴∠ANB＝90º

MA⊥BCAM＝AP/2＝BC/2

⑵延长AM 到P使AP＝BC连接PE,PG .∵AM⊥BC∴∠PAE＝ABC⊿EAP≌⊿ABC﹙SAS﹚

EP＝AC＝AG,∠PEA＝∠CAB＝180º-EAG∴EP∥AG﹙同旁内角互补﹚.AGPE是平行四边形.M是EG中点.