如图,在梯形ABCD中AD∥BC,DC⊥BC,E为AB的中点.求证EC=ED

证：延长DE到F使FE=ED.连接FB∵AD‖BC∴∠BAD=∠FBA,∠BAD+∠ABC=180°∴∠FBA+∠ABC=180°∴FBC三点共线∵∠FBA=∠BAD,BE=AE,∠FEB=∠AED∴△FBE≌△DAE∴EF=ED.∵BC⊥CD∴∠C=90°又∵FE=FD∴CE=FD=EF∴ED=EC 这道...