Question

1. reasoning why do vertices connected by a diagonal of a polygon have to be nonconsecutive

Explanation:

A diagonal of a polygon is defined as a line segment connecting two non - adjacent (non - consecutive) vertices. The sides of a polygon are the line segments that connect consecutive vertices. If we were to connect consecutive vertices, that line segment would simply be a side of the polygon, not a diagonal. So, by the definition of a diagonal (a line segment in a polygon that is not a side), the vertices connected by a diagonal must be non - consecutive.

Answer:

Vertices connected by a diagonal of a polygon must be non - consecutive because the line segments connecting consecutive vertices are the sides of the polygon, and a diagonal is defined as a line segment in a polygon that is not a side.