A triangle has zero diagonals. Diagonals must be created across vertices in a polygon, but the vertices must not be adjacent to one another. A triangle has only adjacent vertices.
A triangle is made up of three lines and three vertex points. Adjacent vertices are those which are not formed from the same line. All of the vertices in a triangle are adjacent to one another, so therefore, a triangle is not formed from any diagonal line segments.
The triangle is the only polygon without diagonals. A quadrilateral, for example, is made up of four lines and four vertex points. It is possible to draw two diagonals, from one non-adjacent vertex to the other, across the center of the quadrilateral.