(Solution) - a The proof that a map that is distance preserving and -(2025 Original AI-Free Solution)

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(a) The proof that a map that is distance-preserving and sends the zero vector to itself incidentally shows that such a map is one-to-one and onto (the point in the domain determined by d0, d1, and d2 corresponds to the point in the codomain determined by those three). Therefore any distance-preserving map has an inverse. Show that the inverse is also distance-preserving.
(b) Prove that congruence is an equivalence relation between plane figures