When renovating the home in the first photo, the architects at Dufner Heighes used the existing geometry of the architecture as an inspiration. The diamond-patterned floor and rug have a gorgeous interplay with the triangle patterns of the fireplace and ceiling.
Unfortunately, we don't all have such striking original architecture to work with, but it's very possible to play around with shapes in other ways, from flooring to furniture. The pattern of a herringbone floor (like the one in the home of Skinny Laminx, fifth photo above) can be echoed in a pillow, or contrasted with a striped rug. A rolling ladder (as in the second photo) can mimic the rectangles in a set of open shelves.
When you're putting together or re-doing a room at home, do you think about the interplay of shapes?