Question

如图,在四边形ABCD中,AB平行于CD,AB=CD,BE=DF（1）说明AE平行于 CF（2）说明AD=BC

Answer 1

(1)∵AB∥CD

∴∠ACE=∠CDF

又∵AB=CD,BE=DF

∴△ABE≌△CDF

∴∠AEB=∠CFD

∴AE∥CF

(2)∵AE∥CF

∴∠AED=∠CFB

又∵BE=DF,BF=BE+EF,DE=DF+EF

∴BF=DE

又∵AE=CF

∴△AED≌△CFB

∴AD=CB