The triangle inequality tells us that given points $x,y,z$ in a Euclidean space (or more generally, in a metric space), $d(x,z)\leq d(x,y)+d(y,z)$ ($d(a,b)$ refers to the distance between points $a$ and $b$).
Use this tag on questions that rely on the triangle inequality in either a geometric or a metric space.
In Euclidean Geometry, the triangle inequality governs the sorts of lengths that can form the sides of a triangle. It says that given non-negative reals $a$ $b$ and $c$, there exists a triangle with side lengths $a$, $b$ and $c$ if $$a\leq b+c,$$ $$b\leq a+c,$$ and $$c\leq a+b.$$ Note that the triangle inequality permits the existence of degenerate triangles.
Mathematicians later realized that this inequality was quite useful in constructing a rigorous notion of distance between points, since in the Euclidean plane, $3$ points form a triangle, and the distances between them serve as the side lengths of the triangle. Hence, in the definition of a metric space, mathematicians introduce a distance function $d:X\times X\to \mathbb R$, where the final condition on the function is that for any $x,y,z\in X$, $$d(x,z)\leq d(x,y)+d(y,z)$$
Use this tag, when either referring to the triangle inequality in a standard Euclidean space or in a more general metric space. Make sure to use the corresponding tags for either metric spaces or Euclidean geometry to indicate what usage of the triangle inequality is relevant.
