If $T$ represents the points that define the perimeter of a triangle and $A = cl (T)$, that is, the closure of $T$, prove that $A$ is a convex set.
Hint: represent $A$ as the intersection of 3 half-planes in $\mathbb{R^2}$, verifying if a hyperplane is a convex set and checking properties relating to union and intersection of convex sets.
I'm really stuck here, I looked at the definitions of half-planes and hyperplane but I do not know where to go