20. In ``The Nine Chapters on the Mathematical Art,'' a quadrangular pyramid with a rectangular base and one lateral edge perpendicular to the base is called a ``yang ma'', and a tetrahedron with all four faces being right triangles is called a ``bie nao''. In the yang ma $\mathrm { P } - \mathrm { ABCD }$ shown in the figure, the lateral edge $\mathrm { PD } \perp$ base ABCD, and $\mathrm { PD } = \mathrm { CD }$. Point E is the midpoint of PC. Connect $\mathrm { DE } , \mathrm { BD } , \mathrm { BE }$.

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\caption{Figure for Question 20}
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(I) Prove that $\mathrm { DE } \perp$ plane PBC. Determine whether the tetrahedron EBCD is a ``bie nao''. If yes, write out the right angle of each face (only conclusions are needed); if no, please explain the reason;\\
(II) Let the volume of the yang ma $\mathr