如图,将矩形纸片ABCD沿其对角线AC折叠,使点B落到点B′的位置,AB′与CD交于点E.
(1)求证:△AEC是等腰三角形;
(2)若P为线段AC上一动点,作PG⊥AB′于G、PH⊥DC于H,求证:PG+PH=AD.