triangle inequality

The triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

Formally,
if $a,b,c$ are the lengths of the sides of a triangle, then

without loss of generality.

\documentclass[tikz,border={2cm 0cm}]{standalone}
\usepackage{tkz-euclide}
%
\definecolor{fillcolor}{HTML}{8A5CF5}
%
\begin{document}
\begin{tikzpicture}
    \tkzDefPoint(0,0){A}
    \tkzDefPoint(3,0){B}
    \tkzDefPoint(1,2){C}
	%
    \tkzDrawPolygon[thick](A,B,C)
    %
    \tkzLabelSegment[below](A,B){$c$}
    \tkzLabelSegment[above right](B,C){$b$}
    \tkzLabelSegment[above left](C,A){$a$}
\end{tikzpicture}
\end{document}