In perspective drawing, everything needs to be exact, (except for organic lines). When I draw perspective in my art class, we require a ruler at all times. The lines all have to be the same length or else it will be out of proportion.
There is a thing called orthographic projection which is a projection used for architects, and engineers. It talks about how all the lines have to be parallel.
This time I substituted the website for a video, and it clearly explains drawing perspective in math. You need geometry, and angles to make sure everything is in proportion.
In one point perspective, when you are drawing the object like a cube, the lines has to create a 90 degree angle. After, the lines that finish up the cube have to be parallel to each other. All of the lines have to be straight too. (unless you are drawing 0 point perspective.)
As you watch the video, you can see that first, the basic shape that defines the soon to be cube is 2d. When you form the cube, it turns into a 3d shape.