The easiest and most common examples of the triangular pattern arise when two enemy pieces are on the same file or rank, often the back rank, with an odd number of squares between them. Start with the simple case of two pieces on the back rank separated by one square—the Black king and rook in the stylized diagram to the left (the diagram is just meant to illustrate how some different bishop forks can work; it doesn't call for consideration of what White should actually play). Black's king and rook are arranged to be forked—by a knight at e6, or by a bishop (or queen) at e7. In the bishop’s case there generally will be an enemy piece already on e7—here, the pawn; otherwise the bishop would be able to take the target piece—the rook—without need of a fork. Now spread the targeted pieces three squares apart (the White king and c1 rook in the diagram). Again a fork is indicated—by a Black knight at e2, or by a bishop or queen at e3.
And a bishop (or queen) fork again is possible if the targets are five squares apart, like the White king and a1 rook. A queen can do the job by moving in directly—say, from d5 to d4 (imagine the White pawn on d4 rather than e3); a bishop can do it by taking an enemy piece sitting on d4, and in this latter case the enemy pieces again will be arranged as a triangle at the outset. And of course all this can happen on a vertical file as well as on a horizontal rank. The horizontal formations just are more common because the pieces start out arranged that way on the back rank and often stay there for a while.