YLL討論網

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#ed_op#DIV#ed_cl#上面好像有點矛盾#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#

我這裡將詳細方法講一下:

作E在DC上使得BE=BC 作F在AC上使得EF=BE. 作G在AB上使得EF=FG

所以角BEC=角BCE=80度 角EBF=EFB=60度.
角FEG=角FGE=40度 角GFA=20度=角GAF
所以 AG=GF=FE=EB=BC 所以 G等於D.
而且BEF是正三角形 所以FG=FB
角GFB=160度 角GBF=10度 所以DBC=70度.

#ed_op#DIV#ed_cl#作AH垂直BC,H在BD上#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#在證AH=BH,得角DBC=70度#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#(註:20-80-80的三角形也很特別,常被出成考題)#ed_op#/DIV#ed_cl#

如圖，△ABC為一等腰三角形，AB=AC，∠A=20°，D為AC上一點，且AD=BC，試求∠DBC