∵ED平分∠ADC∴∠1=∠ADC/2∵EC平分∠BCD∴∠2=∠BCD/2∴∠ADC+∠BCD=2(∠1+∠2) ∵∠1+∠2=90∴∠ADC+∠BCD=180∴AD//BC∴∠A+∠B=180∵AB⊥BC∴∠B=90∴∠A=90∴AD⊥AB
