Scalene Triangle
A scalene triangle has all three sides of different lengths and all three angles of different measures.
Definition
A scalene triangle has all three sides of different lengths and all three angles of different measures, no two sides match and no two angles are equal, and it has no lines of symmetry. The longest side is always opposite the largest angle and the shortest side opposite the smallest, a relationship coming from the law of sines $a/\sin A = b/\sin B = c/\sin C = 2R$; formally, a scalene triangle has pairwise distinct side lengths, implying pairwise distinct angles and a trivial symmetry group.
Example
A triangle with sides $3$ cm, $5$ cm, and $7$ cm is scalene, no side matches another and no corner matches another. A triangle with sides $5, 8, 11$ has angles approximately $25^\circ$, $45^\circ$, and $110^\circ$ (obtuse scalene), and since the largest angle is obtuse, the side opposite it ($11$) is the longest, consistent with the side-angle relationship. For sides $a=6$, $b=9$, $c=11$: $s=13$, area $=\sqrt{13\cdot7\cdot4\cdot2}=\sqrt{728}\approx26.98$, and since $11^2=121>36+81=117$, angle $C$ is obtuse.
Key Insight
The word "scalene" comes from Greek meaning "unequal," and most triangles drawn randomly turn out scalene, it is actually the most common type, since equal sides require careful construction. Scalene triangles are the "generic" case in the moduli space of triangles, the space of all triangles up to similarity: scalene triangles form an open dense subset of that space, while equilateral and isosceles triangles are special, measure-zero boundary cases.