Question

如图,已知△ABC∽△DEF,△ABC与△DEF的相似比是3:2,点G,H分别在BC,EF上,且BG:GC=EH:HF,求AG:DH的值.

如图,已知△ABC∽△DEF,△ABC与△DEF的相似比是3:2,点G,H分别在BC,EF上,且BG:GC=EH:HF,求AG:DH的值.

Answer 1

由BG/GC=EH/HF得，GC/BG=HF/EH,等式两边加1,得(GC+BG)/BG=(HF+EH)/EH
即BC/BG=EF/EH。所以BG/EH=BC/EF=3/2，由△ABC∽△DEF得 角B=角E，
AB/DE=3/2=BG/EH,故△ABG∽△DEH.所以AG/DH=AB/DE=3/2

Answer 2

3/2

Answer 3

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