Question

why does the triangle not have a diagonal​

Answer 1

A diagonal of a polygon is a line from a vertex to a non-adjacent vertex. So a triangle, the simplest polygon, has no diagonals. You cannot draw a line from one interior angle to any other interior angle that is not also a side of the triangle.

Answer 2

Triangle doesn't have any diagonal because a figure need 4 sides to have a diagonal, but triangle is made of 3 sides. Ex. Square, Rectangle, Trapizium has diagonals.