An emotional triangle is the building block of the system, and it involves three individuals and how they interrelate to each other.
We can think of a larger system as interlocking triangles.
There are four triangles in a four-person family (Mom, Dad, Sister and Brother): 1) Mom, Dad and Sister; 2) Mom, Dad and Brother; 3) Sister, Brother and Mom; 4) Sister, Brother and Dad.
When the relationship between two people (Mom and Dad) has a problem, one of them or both may seek out a third party to talk with instead of resolving that problem amongst themselves.
Think of a Wife who is frustrated with her Husband's drinking, worried, and feels alone. Because she feels she can't speak to him but needs to talk to someone, she shares how she feels about the Husband/Dad with her Daughter. Which brings the third person into the parents' relationship and forms an emotional triangle. This will affect the Daughter's relationship with her Dad as she will likely align herself with her Mom and take on her Mom's feelings.
Then the Brother starts acting out; maybe he doesn't feel as connected to the family because Mom and Sister are so close because Mom confides in the Sister. Mom and Dad get frustrated with Brother's behaviour. And they bond and pull closer because the Brother is a trouble-maker, creating another triangle (Mom, Dad, Brother).
Now, Sister is upset because she took Mom's side and supported Mom. But now Mom and Dad are close again, and Mom isn't confiding in her and treating her special anymore, and it is all Brother's fault (triangle between Sister, Mom and Brother).
The Brother ends up becoming the Scapegoat in the family. Family systems get very complicated when we consider the emotional triangles between adults and their parents and their spouse, their in-laws, their adult siblings and the sibling's family and their parent's siblings (Aunts and Uncles).
These patterns come out of the family system and are recreated in friend groups and workplaces. Emotional Triangles are going on everywhere. It becomes a way to deal with relational anxiety.