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How can we set the same color for a surface and a 3D parametric curve in version 9? Here is an example below.

Show[{Plot3D[-y, {t, -1, 0}, {y, -1, 1}, Mesh -> None], 
  ParametricPlot3D[{1, -t, t}, {t, -1, 1}, 
   PlotStyle -> {Thick}]}, PlotRange -> All]

More precisely, how can we determine the color of the surface and set it to the black line?

surface and line

J. M.'s missing motivation
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