I am reading the proof of the Simplicial Approximation Theorem (2C.1) in Hatcher.
In the first paragraph of the proof, Hatcher says that:
Choose a metric on $K$ that restricts to the standard Euclidean metric on each simplex of $K$. For example, $K$ can be viewed as a subcomplex of a simplex $\Delta ^N$ whose vertices are all the vertices of $K$, and we can restrict a standard metric on $\Delta ^N$ to give a metric on $K$.
Here $K$ is just a finite simplicial complex.
I understand that the second sentence clearly implies the first, but I cannot understand why we can view $K$ as a subcomplex of a simplex $\Delta ^N$. Any help?