I would use the line tool to cut each one diagonally. Then I would select the background and invert and copy onto a new image the same size, aligning the pieces precisely (you can zoom up to see what you're doing better).
You can do that in about any graphics editor.
I use layers so I would just diagonally divide one, delete the part I don't want, put it on the top layer with the other photo on the bottom, merge and save.
Probably better not to use the anti-alias feature; the two should blend together ok. There are lots of different ways to do things.
I forgot to tell you you will have to select and delete, and I can do it but offhand can't figure out an easy way. I would probably use a blank template the same size, draw the diagnonal, make sure there are no open ends, then use the magic wand on the deleted part, save the selection, make the other image active, then load the saved selection into that image and delete the part you don't want, you may have to invert selection. Sorry if I've confused you. I do most new things on the fly and figure out a way as I go along because I've been doing it a long time.
I'd prefer to resize when I'm almost done, not to try to get the pieces to fit.