What I did when I first saw this problem is graphed it very carefully myself. You can easily see that it should not be a straight line. You can do it on a computer if you have a drafting program. But someone who wants to make it a straight line can draw it as a straight line. The fact that the point where the two triangles meet is
not on the straight line from the top of the upper triangle to the bottom of the lower triangle should be clear if the graph is correct. What I am saying is that a thick line can hide the fact where a very thin line will show it.
If I was making a drawing to fool people, I would use thick lines and draw it so the two triangles looked like they joined in a straight line. Try graphing the shapes and fitting them together. I think you can convince yourselves.