当点A和点E在BC的同侧时,AE与BC一定平行.
证明:
在△ABE和△CBD中,
AB = CB ,∠ABE = ∠EBD -∠ABD = 60°-∠ABD = ∠ABC-∠ABD = ∠CBD ,BE = BD ,
所以,△ABE ≌ △CBD ,
可得:∠BAE = ∠BCD = 60° = ∠ABC ,
所以,AE‖BC .
当点A和点E在BC的同侧时,AE与BC一定平行.
证明:
在△ABE和△CBD中,
AB = CB ,∠ABE = ∠EBD -∠ABD = 60°-∠ABD = ∠ABC-∠ABD = ∠CBD ,BE = BD ,
所以,△ABE ≌ △CBD ,
可得:∠BAE = ∠BCD = 60° = ∠ABC ,
所以,AE‖BC .