Hitch,

The Heidelberg Catechism answers it this way. The entire Catechism is found together with Ursinus' Commentary, in the Devotions section. The section dealing with this question is found here.

V. What kind of bodies shall rise in the resurrection?

The bodies with which we shall rise in the resurrection, will not only be human bodies, but also the very same which we now have, and not other and different bodies created by Christ, as the Anabaptists affirm. Job says, “In my flesh shall I see God.” (Job 19:26.) The apostle Paul says, “Everyone shall receive in his body according to that he hath done;” “and this mortal shall put on immortality.” (Eph. 6:8. 1 Cor. 15:53.) It was therefore, taught in the African churches: I believe in the resurrection of this flesh. The same thing may be argued from the import of the word resurrection: for nothing can rise again, except that which has fallen. “This is the resurrection” said Ambrose, “as may be inferred from the import of the word itself, that that which fell may rise, and that what was dead may revive” The justice of God also establishes the same thing.  “For this” said Ambrose, “is the order and course of justice, that since every action is common both to the body and the soul, the body executing that to which the soul prompts, it is proper that both should come into judgment, and that both should either be given over to punishment, or crowned with glory “The justice of God demands that the bodies of the saints which have fought, should also be crowned; and that the wicked be punished in the same bodies in which they have blasphemed and opposed God. Wherefore, there will be restored in the resurrection to every soul, not a strange and different body, but its own proper body that which it here had and shall thus be crowned with glory, or punished with shame.  Finally, as Christ rose with the same body which he had when he died, so shall we also rise with the very body which we now have.

The Chestnut Mare