#### Question

Given the right trapezoid ABCD , AB\parallel CD , AB\perp AD , AB=AD=\dfrac{1}{2}CD=1 . Now make a square ADEF with AD as one of its sides, and then fold the square along AD to make the plane ADEF is perpendicular to plane ABCD , M is the midpoint of ED .

(1) Prove AM\parallel plane BEC ;

(2) Prove BC\perp plane BDE ;

(3) Find the distance from D to plane BEC