底角为30度的等腰三角形ABC,AB=AC:
1,
作AD⊥BC,垂足D,
AB=AC,AD=AD,∠B=∠C,∠ADB=∠ADC=90°,∠BAD=90°-∠B=90°-∠C=∠CAD,
△ABD≌△ACD,[SAS]
RT△ABD∽RT△ACD,[AAA,相似比=1];
2,
BC上一点D,使BD=CD,连接AD,
AB=AC,AD=AD,BD=CD,
△ABD≌△ACD,[SSS]
∠B=∠C,∠ADB=∠ADC=180°/2=90°,∠BAD=∠CAD,
RT△ABD∽RT△ACD,[AAA,相似比=1];
3,
作∠A的平分线交BC于D,
∠B=∠C,AB=AC,∠BAD=∠CAD,AD=AD,
△ABD≌△ACD,[ASA]
∠ADB=∠ADC=180°/2=90°,
RT△ABD∽RT△ACD,[AAA,相似比=1];