Question

for which of the following polygons can the triangle inequality theorem be applied to determine if they can exist?
a. circle
b. square
c. hexagon (regarding its diagonals forming triangles)
d. any triangle

Explanation:

The Triangle Inequality Theorem is specifically about triangles. It states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. This theorem is fundamental in determining if a set of three lengths can form a triangle. A circle is not a polygon. While a square or hexagon (regarding its diagonals forming triangles) may involve triangles in some analysis, the theorem is directly and primarily applied to triangles.

Answer:

d. Any triangle