Being able to "make a triangle" with your king is a very important concept in King+Pawns VS King+Pawns endgames. Sometimes, having a square to make the triangle can make a difference between a won position and a drawn one. For example, I was able to won this game because my opponent couldn't make the triangle:
BTW, notice that 37.c5+ ! that seems a bad move making d5 a weak square, is actually necessary sooner or later. For instance, 37.Kd3 Kd7 38.d5 ?? c5 !! = (despite the advanced passed pawn, the white king cannot go through the pawn mass !)