The best real life example I can provide is that the practice of quilting involves bisecting angles. If you look at any quilt, you will likely see triangles.
The second best example I can provide involves sewing with plaid or striped material. Sometimes the sewer wants to cut-on-a-bias. This involves a diagonal cut of the fabric. If you look at one of the photographs of me, you will see me wearing a plaid suit I made for myself. It is NOT bias-cut because I did not have enough fabric. The lines of the plaid are vertical and horizontal.
When making a skirt, sometimes the components are triangular-shaped, without the peak of the triangle. For design purposes, I may want to bisect a component and make each resulting component of a different fabric, particularly if I am working with remnants and each remnant is too small for one original component. I may also want to make each resulting component a different orientation of the same fabric. For example, if I am working with stripes, perhaps the lines of one with be positive and the lines of the other with be negative-inverse, also known as perpendicular.
For other real life examples, I suggest you ask a carpenter.