#### Question

Given the pyramid P- ABCD , AB⊥ plane PAD , AB\parallel CD , PD=AD , point E is the midpoint of PB , F is on CD , DF=\dfrac{1}{2}AB , PH is the height of △PAD originating from side AD .

(1) Prove PH⊥ plane ABCD

(2) If PH=1 , AD=\sqrt{2} , FC=1 , find volume of three sided pyramid E-BCF .

(3) EF⊥ plane PAB