How to apply Cauchy's Residue Theorem to a triangle?

Question

Say I have a triangle with vertices $(-5, 5, 17i)$ and a function $f(z)$ with a residue of $-\dfrac{i}{5}$. Would I apply the residue theorem once and end up with $2 \pi i \cdot -\dfrac{i}{5}$ or would I apply it on every line segment so $2 \pi i \cdot -\dfrac{i}{5}$ + $2 \pi i \cdot -\dfrac{i}{5}$ + $2 \pi i \cdot -\dfrac{i}{5}$?

Answer 1

You would apply it once with the contour being the entire triangle. It doesn't make sense to apply it to each segment of the triangle because the theorem is for closed contours.