Question

What is true about an equiangular polygon and its relation to being equilateral?

a) An equiangular polygon is always equilateral
b) An equiangular polygon is never equilateral
c) Equiangular and equilateral are unrelated
d) Equiangular implies equilateral and vice versa

Answer 1

Option (d), Equiangular polygon implies equilateral and vice versa, which holds true particularly for regular polygons where all sides and angles are equal.

Step-by-step explanation:

The question asks about the relationship between equiangular polygons and equilateral polygons. An equiangular polygon is one where all angles are equal, whereas an equilateral polygon is one where all sides are of equal length.

In many cases, especially with regular polygons, an equiangular polygon will also be equilateral, meaning that all sides are equal because the angles are all equal. However, unless the polygon is regular, a polygon being equiangular does not always imply that it is equilateral, or vice versa.

Thus, the most accurate statement regarding the relationship between equiangular and equilateral polygons is: d) Equiangular implies equilateral and vice versa. This is true for regular polygons, where the term regular implies that the polygon is both equiangular and equilateral.