∵BE平分∠ABD
∴∠1=∠ABE=½∠ABD
∵DE平分∠BDC
∴∠2=∠CDE=½∠CBD
∵∠1+∠2=90°
∴∠ABE+∠CDE=90°
∴∠ABE+∠CDE+∠1+∠2=180°
∴AB∥CD