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];