If that is true what does the render actually show when a folded quad is viewed at a skewing angle?>>539444
Doesn't need to be converted. A quaded model is always triangulated. You just look at what is called an 'isoline display' in software like maya.
A view that hide certain edges for you the human editor so you can more easily read the structure of the surface.
The reason you attempt to quad things is that this generates a surface with evenly spaced triangles as all the triangles are paired with another and of similar size.
This makes for few points on the surface where more than 4 edges meet at the same vertex at what is commonly called a 'pole'.
Having poles where many edges meet creates messy geometry when the model subdivided and cause pinching artifacts in the shading of the surface.
Poles cannot be avoided completely but A well quaded model minimize them to a few 5-pole vertices.
(Also once you understand why you actually want a quaded surface you no longer need to use quaded surfaces and instead insert triangles to your geometry where they make sense.)