I've noticed that in Object Mode, if you select an object it will tell you how many triangles are in the mesh. However, is there a way to highlight where they are? From what I can see, everything is made out of quads. It says the same thing for the default cube as well.
Triangle count refers to the tessellated result of the final mesh, required by graphics cards to draw geometry, not necessarily your mesh polygons.
A four sided face will be made up of two triangles, even though no three sided faces are present in your model.
To find all three sided faces faces in one mesh, while in Edit Mode select one of the triangles, the use the Select Similar operator Shift + G > Polygon Sides.
Or If one can't easily be found, do the inverse process, select a quad, then invert selection with Ctrl + i.