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A parallelepiped S has base points A ,B ...

A parallelepiped `S` has base points `A ,B ,Ca n dD` and upper face points `A^(prime),B^(prime),C^(prime),a n dD '` . The parallelepiped is compressed by upper face `A ' B ' C ' D '` to form a new parallepiped `T` having upper face points `A prime prime,B prime prime,C prime prime `and `D prime prime` . The volume of parallelepiped `T` is 90 percent of the volume of parallelepiped `Sdot` Prove that the locus of `A"` is a plane.

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A parallelepiped S has base points A ,B ,Ca n dD and upper face points A^(prime),B^(prime),C^(prime),a n dD ' . The parallelepiped is compressed by upper face A ' B ' C ' D ' to form a new parallepiped T having upper face points A",B",C"a n dD" . The volume of parallelepiped T is 90 percent of the volume of parallelepiped Sdot Prove that the locus of A" is a plane.

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