解答：证明：（1）∵四边形ABCD是等腰梯形，∴AB=CD，∠ABC=∠DCB．又∵BE=CF，∴△ABE≌△DCF．∴AE=DF；（2）∵BE=CF，∴BF=CE，又∵AB=CD，∠ABC=∠DCB，∴△ABF≌△DCE，∴AF=DE．又∵AD=EF，AD∥BC，∴四边形AEFD为平行四边形．∴四边形AEFD为矩形．
