Question

已知,△ABC中,AB=AC,∠BAC=108°,BD平分∠ABC,求证：BC=AB+CD

Answer 1

在BC上截取BE=AB,连接DE

∵AB=AC

∴∠ABC=∠C=(180°-108°)/2=36°

∵BD平分∠ABC即∠ABD=∠DBE

BD=BD,AB=BE

∴△ABD≌△BDE

∴∠BED=∠BAC=108°

∴∠DEC=180°-∠BED=180°-108°=72°

∴∠EDC=180°-∠DEC-∠C=180°-72°-36°=72°

∴∠DEC=∠EDC

∴CD=EC

∵BC=BE+EC

∴BC=AB+CD