Question

已知AB=DC,AE=DE,BE=CE,求证:AD平行BC

Answer 1

因为AB=DC,AE=DE,BE=CE

所以△ABE≌△DCE

∴∠AEB=∠DEC

∠AEB+∠DEC+∠AED=2∠AEB+∠AED=180°

因为AE=DE

∠EAD=∠ADE

∠EAD+∠ADE+∠AED=2∠EAD+∠AED=180°

∴∠AEB=∠EAD

所以：AD//BC