Question

如图示,在△ABC中已知:AD是∠A的平分线,求证:AB比AC=BD比DC

Answer 1

证明：过点B做BE∥AC，交AD的延长线含银与点E
∵BE∥AC
∴
∠BED=∠DAC
∵AD是芹升∠A的平分线
∴∠BAD=∠DAC
∴∠BED=∠BAD
AB=BE
∵
∠BED=∠DAC
∠BDE=∠ADC
∴△BDE∽△ADC
BD:CD=BE:AC
∵
AB=BE
∴BD:CD=AB:AC
即谈首宴BAB:AC=BD:CD

Answer 2

延世腊长AD
再其延长线上取一点E，使BE=BD
△漏喊BDE为
等搜搜滑腰三角形

∠BED=∠BDE=∠ADC
又∠BAD=∠DAC
∴△ABE∽△ACD
∴AB:AC = BE:DC
∵BE=BD
∴AB:AC = BD:DC