TITLE: How many triangles in picture
QUESTION [8 upvotes]: How many triangles in this picture:

I know that I can just count the triangles to solve this specific problem. I would be interested to know if there is a systematic approach to doing this that can be generalized to larger diagrams of the same type.

REPLY [21 votes]: I know there's already an excellent answer from Brian M. Scott... Buuuuut...
Here's a visual supplement to the aforementioned systematic brute force.