Is this statement true or false? In a regular polygon, two consecutive radii and their included side form an equilateral triangle. false true

**False.** In a regular polygon, the statement that two consecutive radii and their included side form an equilateral triangle holds true **only** for a regular hexagon. Here's why: - **Regular Hexagon (6 sides):** - Each central angle is 60 degrees. - The length of each side is equal to the radius (\( R \)) of the circumscribed circle. - Therefore, the triangle formed by two consecutive radii and the included side is equilateral. - **Other Regular Polygons:** - For polygons with a different number of sides (e.g., equilateral triangle with 3 sides, square with 4 sides, etc.), the relation does not hold. - For instance, in a square (4 sides), the side length is \( \sqrt{2}R \), which is not equal to the radius \( R \), making the triangle isosceles but not equilateral. Since the statement is not universally true for all regular polygons, it is **false**.