△ABC是等腰三角形,AC=BC,E,F分别为AC,AB的中点,将△AEF沿EF折起,使A‘在平面BC求证；EF⊥A'C

Question

△ABC是等腰三角形,AC=BC,E,F分别为AC,AB的中点,将△AEF沿EF折起,使A‘在平面BC求证；EF⊥A'C

Answer 1

题目有误 应该求证的是EF⊥A'A
明显EF‖A'C
设EF和A'A交点为P
△AEF≌△A'EF
AF=A'F
AE=A'E
∠EAP=∠EA'P
△AEP≌△A'EP
所以∠EPA=∠EPA'
所以∠EPA=90°
所以EF⊥A'A