已知 如图,E为BC上一点,AC//BD,∠D=∠ABC,试说明∠ABD=∠CED

Question

已知 如图,E为BC上一点,AC//BD,∠D=∠ABC,试说明∠ABD=∠CED

Answer 1

1、∵∠ABC=∠D
∴∠CED=∠EBD+∠D=∠ABC+∠EBD=∠ABD
2、∵AC∥BD
∴∠ACB=∠EBD
∵∠ABC=∠D
∴△ABC∽△EDB
∴∠A=∠BED
∵∠A+∠ABD=180°
∠CED+∠BED=180°
∴∠CED=∠ABD