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 $$ PAB $$

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 $$ PAB $$

Question