Question

1. for which of the following polygons can the triangle inequality theorem be applied to determine if they can exist?

a. circle
b. any triangle
c. hexagon (regarding its diagonals forming triangles)
d. square

Explanation:

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. This theorem is specifically designed for triangles. A circle is not a polygon with sides for this theorem to apply. While a hexagon's diagonals can form triangles, the theorem is most directly and inherently applicable to any triangle itself. A square is a quadrilateral, and the theorem is not used to determine its existence in the same fundamental way as for a triangle.

Answer:

B. Any triangle