How to change uv map from squares to triangles?

Hi there,

I triangulated my mesh but in the uv map it’s still showing as squares, how could I make it to be triangles as well? I searched online but couldn’t find any answers, any help would be appreciated!

This is my mesh and uv map, and at the bottom right is what I’d like to have

Your mesh is not triangulated. The Triangulate modifier (and any other modifier) does not change the mesh data until you apply it.