初二相似图形,如图,在四边形ABCD中,延长AB到点E,延长AD到点G,链接AC并延长到点F,使得BE=AB,DG=AD,CF=AC,

Question

初二相似图形,如图,在四边形ABCD中,延长AB到点E,延长AD到点G,链接AC并延长到点F,使得BE=AB,DG=AD,CF=AC,

Answer 1

∵四边形AEFG∽四边形ABCD
∴BE=AB,DG=AD,CF=AC
∴CD是三角形AFG的中位线
CD‖FG
AD/AG=AC/AF=CD/FG=1/2
∠ACD=∠AFG,∠ADC=∠AGF
BC是三角形AEF的中位线
BC‖EF
AB/AE=C/AF=C/EF=1/2
∠ABC=∠AEF,∠ACB=∠AFE
AD/AG=CD/FG=BC/EF=AB/AE=1/2
∠DAB=∠GAE,∠ADC=∠AGF,∠DCB=∠DFE,∠ABC=∠AEF
四边形AEFG与四边形ABCD是相似图形