  Let $X$ be a real analytic orbifold. Then each stratum of $X$ is a
subanalytic subset of $X$. We show that $X$ has a unique subanalytic
triangulation compatible with the strata of $X$. We also show that every ${\rm
C}^r$-orbifold, $1\leq r\leq \infty$, has a real analytic structure. This
allows us to triangulate differentiable orbifolds. The results generalize the
subanalytic triangulation theorems previously known for quotient orbifolds.
