已知:如图,在Rt△ABC中,∠C=90°,∠BAD=½∠BAC,过点D作DE⊥AB,DE恰好是∠ADB的平分线,求证：CD=½DB.

Question

已知:如图,在Rt△ABC中,∠C=90°,∠BAD=½∠BAC,过点D作DE⊥AB,
DE恰好是∠ADB的平分线,求证：CD=½DB.

Answer 1

∵∠A＝∠BDE=∠ADE
∠ADC=90º-½∠A
∠BDE∠BDE+∠ADC=180º
∠A+∠A+90º-½∠A=180º
∠A=30º
CD=DE=½BD