过点G作GM⊥AC于点M,DN⊥BC于CB的延长线于点N,连接GA,GB∵DG是AB的垂直平分线∴GA=GB∵CG是∠ACB的角平分线∴GM=GN∴RT△AMG≌RT△BNG∴∠AGM=∠BGN∴∠AGM+∠MGB=∠BGN+∠MGB=∠MGN=90°即∠AGB=90°∴△AGB是等腰...