When I was school, I remember being given a task during science (maybe) to make a bridge using just lolly sticks, newspaper and glue. As a class we tested to see how much weight each bridge could hold. It must have been a good lesson because here I am 30 or so years later thinking about it. From that lesson, I learned that triangles are great structures for building bridges; they distribute the weight from a single point to a wide base.
Years later, I would learn that they are also great for building poses. We've all seen (and created!) those photographs where people are lined up in a straight line horizontally. It's an easy way to pose people especially if there are lots of people in the group and you're pushed for time. However to the viewer it's not such an interesting composition. Their eyes literally has to travel from left to right before losing and there is nothing to keep them interested to flow throughout the image. When we create photographs, we want the eye to linger; we want to encourage the eye to flow throughout the picture.
I've talked about how curves in a photograph can take viewer's the eye on a more interesting journey encouraging their eyes to remain on the form; triangles do a similar job.
For groups creating triangles with the subjects' heads is a good way to create a more interesting composition, it makes the photograph look balanced, it also creates a more intimate photograph.
Triangles can also play a part in individual's poses by making use of their limbs. This is great news because most if not all people I've worked with want to know what they should do with their hands. People being photographed are far more comfortable if they are given something to do with their hands.
There are lots of ways to create triangles and you will find that you may even be creating some without thinking about it. Here are a few examples to try.






As with the bridges, the triangles created gives rise to a sense of stability and power to the pose as well as providing more interesting shape for the eye to follow and flow through the picture.