Question

如图所示,在△ABC中,∠B=2∠C,AD为角平分线,请说明AC=AB+BD的理由

Answer 1

延长AB到E,使BE=BD,连接DE,

则∠E=∠BDE,∠ABC=∠BDE+∠E=2∠E,

∵∠ABC=2∠C；∴∠C=∠E,

∵∠DC=∠DAE,AD=AD,

∴ΔADE≌ΔADC,

∴AC=AE,

即AC=AB+BD.