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Find geometric shape

Hi guys"

I have to following issue:

I have an arbitrary polygon (defined with points A,B,C,D,...) and I want to find the position of this polygon in "real" images: In these images the polygons are not ideal geometric shapes, but physical objects.

For instance the polygon might be a right-angled triangle and I then want to detect "set squares" in an image + its rotation.

Do you know any solutions to this problem? I already tried to do this with SURF and SIFT where I would simply paint an artifical image with my polygon and extracting features of this artifical image, however the extracted feature do not seem to work quite well. Template matching with an artifical image is not working either, because the objects in the real images can be rotated.