(1)在图1中,作DE⊥AB,DF⊥AC, ∵AD平分∠BAC, ∴DE=DF, ∵S△ABD=AB×DE,S△ACD=AC×DF, ∴S△ABD:S△ACD=AB:AC. 故答案案为:DE=DF,AB、DE,AC、DF,AB:AC;
(2)在图2中,作AP⊥BC, ∵S△ABD=BD×AP,S△ACD=CD×AP, ∴S△ABD:S△ACD=BD:CD; 故答案为:BD、AP,CD、AP,BD、CD;
(3)∵(1)中,S△ABD:S△ACD=AB:AC, 在(2)中,S△ABD:S△ACD=BD:CD, ∴AB:AC=BD:CD. 故答案为:AB、AC、BD、CD. |