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

To determine whether the statement is true or false, let's analyze it step by step. 1. **Understanding the terms**: - A **regular polygon** is a polygon with all sides and angles equal. - A **radius** of a polygon refers to the distance from the center of the polygon to any of its vertices. - The **included side** refers to the side of the polygon that is between two consecutive radii. 2. **Visualizing the scenario**: - In a regular polygon, if we take two consecutive vertices and draw the radii to these vertices, we form a triangle with the included side (the side of the polygon connecting these two vertices). 3. **Analyzing the triangle**: - The two radii are equal in length (since they are both radii of the same circle). - The included side is the side of the polygon, which may or may not be equal to the lengths of the radii. 4. **Conditions for an equilateral triangle**: - For the triangle formed by the two radii and the included side to be equilateral, all three sides must be equal. - This is only true in specific cases, such as in an equilateral triangle itself or in a regular polygon with a specific number of sides (like a triangle). 5. **Conclusion**: - In general, for a regular polygon with more than three sides, the included side will not equal the lengths of the radii, thus not forming an equilateral triangle. Therefore, the statement is **false**.