How may I find the line segment formed that two 3D triangles in certain collision make?

Assuming the facts are that two 3D triangles are not parallel, nor perpendicular, any one's edge or point(s) do not share an edge or point(s) of the other. The triangles are in collision and have not split more than one edge of another. i.e. the image below satisfies all these conditional facts.

Having said that, my question is what is for the formula for getting the (red) points of the (green) line segment formed. I'm certain there was a way with the Pythagorean theorem, or similar to it, and possibly averages of the points data somehow, but without the HTML page I found the help on, a teacher's personal website that I no longer can find, I am at a loss. Can anyone help?

Looking at the image above, I think to myself, it should be so simple, right there exploited. But it's not.