Why does a triangle not have 4 sides?

Answer: A triangle is a polygon formed by connecting three non-collinear points with straight line segments, and by definition, it inherently has only three sides.

A triangle is a fundamental geometric shape consisting of three straight sides and three angles. It is a polygon with the fewest number of sides. The definition of a triangle is based on having precisely three sides; therefore, it cannot have four sides.

In Euclidean geometry, a triangle is formed when three non-collinear points are connected by straight-line segments. Each line segment between two points forms one side of the triangle. Since there are only three distinct points involved, there can only be three sides to the triangle.

Furthermore, the properties and characteristics of triangles, such as the sum of the interior angles being equal to 180 degrees and the existence of various types of triangles (e.g., equilateral, isosceles, scalene), are all based on the fact that a triangle has three sides. Adding a fourth side would fundamentally change the shape and properties, resulting in a different polygon altogether.

In summary, a triangle is defined as a polygon with three sides, and its very definition precludes the possibility of it having four sides.