∫AB∨CD

∴∠F=∠ABE,∠FDE=∠A

Divide equally ∠ABC

∴∠ABE=∠CBE

∴∠F=∠CBE

∴BC=FC

Ce sharing ∠BCD

∴ be = ef (three in one)

∴△FDE≌△BAE

∴DF=AB

∫FC = DF+CD

∴FC=AB+CD

∴BC=AB+CD