Well I know that the Gromov-Hausdorff distance between isometric spaces is 0. But I don't know how can I prove it. Well, if I use the following definition of Gromov-Hausdorff distance:
If X,Y are metric spaces, the $d_{GH}(X,Y)$ is the infimum value of $r > 0$ where exists a metric space $Z$ with $X',Y' \subset Z$ and isometric to $X$ and $Y$ respectively and $d_H(X',Y') < r$.
Well, if I use the definition I have that $X$ and $Y$ are isometric so $X'$ and $Y'$ are also isometric. So now I have to prove that $d_H(X',Y') = 0$ but I don't know how can I do it.
Take $Z=X$, $X'=X$, and $Y'=X$. Then $d_H(X',Y')=0$.