You could look at this code on FileExchange, which appears to support triangles and squares:
It's been years since I did anything with the hough transform, but from memory if you want to find rectangles (or indeed ellipses) you need to search a range of possible width/height ratios or hard-code the width/height ratio that you are looking for. I think even with regular geometry like squares and circles you still need to specify a width/radius.
