I don't think regionprops would help. regionprops() measures regions. It might be able to find triangle-shaped regions for you, but as far as taking a single triangle and finding which pixels are at the corner, it can't do that. What about using the corner() function? Have you tried that? Or look at bwboundaries() and try to identify sharp turns.
And, of course, posting an image never hurts. In fact, it's usually mandatory.