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A triangle is a three-sided polygon, while a diagonal is a line connecting two non-adjacent vertices of a polygon. A triangle has no diagonals because it only has three sides and three vertices, so it is impossible to draw a line connecting two non-adjacent vertices.

The triangle is the simplest and most basic of all polygons, and it is the only polygon that does not have a diagonal. This is because a triangle has the fewest number of sides and vertices of any polygon, so it is impossible to draw a line connecting two non-adjacent vertices.

The fact that a triangle does not have a diagonal is an important property of triangles that is used in many different areas of mathematics. For example, in trigonometry, the angles of a triangle can be determined by the lengths of its sides, and this property is only possible because a triangle does not have a diagonal.

In conclusion, a triangle does not have a diagonal because it only has three sides and three vertices, and this property is used in many different areas of mathematics.