Thanks everyone for the explanation to the triangle puzzle... shortly after I posted that last link Chris and I figured it out and bonked ourselves on the heads. We realized that the angles of the two triangles were not the same, thus causing a slight curve on the hypotenuse of the triangle as a whole that was not easily visible to the naked eye. Thank you Phil @ Fibiger.org for the slope information. Being out of school for so long made me a little rusty when it comes to simple geometry.

Back to job hunting. :)