This is the first problem that a student meets in most American geometries.
The number of geometries compatible with these premises will be limited.
For instance, we might know that in non-Euclidean geometries, parallels meet.
The real criterion then of all geometries is neither truth, conformability nor necessity, but consistency and convenience.
The branch of mathematics that treats the properties, measurement, and relations of points, lines, angles, surfaces, and solids. (See Euclid and plane geometry.)