19. In a right triangular prism $A B C - A _ { 1 } B _ { 1 } C _ { 1 }$, the lateral face $A A _ { 1 } B _ { 1 } B$ is a square. $A B = B C = 2$. Let $E , F$ be the midpoints of $A C$ and $C C _ { 1 }$ respectively, and $B F \perp A _ { 1 } B _ { 1 }$. (1) Find the volume of the triangular pyramid $F - E B C$; (2) Let $D$ be a point on edge $A _ { 1 } B _ { 1 }$. Prove that $B F \perp D E$. [Figure]
19. In a right triangular prism $A B C - A _ { 1 } B _ { 1 } C _ { 1 }$, the lateral face $A A _ { 1 } B _ { 1 } B$ is a square. $A B = B C = 2$. Let $E , F$ be the midpoints of $A C$ and $C C _ { 1 }$ respectively, and $B F \perp A _ { 1 } B _ { 1 }$.\\
(1) Find the volume of the triangular pyramid $F - E B C$;\\
(2) Let $D$ be a point on edge $A _ { 1 } B _ { 1 }$. Prove that $B F \perp D E$.\\
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