Our stories often have similar elements to triangulation. Take for example our MC has two companions who are wanting to go a different way. The MC sees value in both of the companions ideas and has a tough time trying to figure out which way is the best for the group.
Triangulation is a great way to also look at alliances and wars. Take for example (very simplified) WWII. There were many alliances formed between nations. One of the nations that had alliances went to war with another nation that had an alliance. This caused a chain reaction that caused all of those aligned with the two nations at war to eventually end up in the war as well.
The more we understand the triangles that are being formed between our characters the more we will understand how they will react to certain situations within the plot.