We all can recognize simple shapes and relations effortlessly, for example, triangles of all sorts, no matter their specific geometric characteristics, be them scalene, equilateral, isosceles, Pythagorean, 30-60-90, or what-have-you. After all, all triangles consist of three lines (edges) connected in three points (vertices). Still, if someone asks the question about how many shapes can be made from three straight line segments that may be connected to one another or not, intersecting one another or not, floating to another or not, the answer is not straightforward. An unambiguous way to classify, retrieve and instantiate 3–, 4–, 5–, 6– and more generally, n-line arrangements to construct shapes will potentially have a great impact in computer shape recognition and CAD applications. The complete calculation of all possible parametric shapes made of 3 lines is given below without counting parallelism and/or intersections of valency greater than 2. All 390 shapes are unique, or otherwise, non-equivalent with respect to the symmetry group of the triangle, that is, there is no symmetry transformation of the Euclidean plane that can map one configuration to another.