Geany currently defaults to using xdvi and xpdf to show TeX files. Since xdvi and xpdf are such old programs they are no longer installed by default on most systems.
Changing the default Geany install to use xdg-open by default would allow Geany to automatically use the user's "preferred application" to open dvi and pdf files. The user can change this himself after installation, of course, but using xdg-open by default would allow it to work out-of-the-box, which is obviously a better result.
Geany 0.21/Centos6
It's now using Evince since this commit[1] (see comments there). We talked about using xdg-open but no one ever did it.
I'm not going to close this though since the bug is still valid even with Evince as the default instead of xdg-open.
[1] https://github.com/geany/geany/commit/d33f511fc49b09168284bfe030f738635f748258