Question

show instructions question 3 (2 points) tell whether the figure is a polygon. if it is not, explain why not. if it is, tell whether it is convex or concave.

Explanation:

Step1: Recall polygon definition

A polygon is a closed figure with at least 3 straight sides, no curved sides, and sides that do not cross each other (except at vertices). The given figure (a star - like shape, a concave polygon or a self - intersecting? Wait, no, this is a concave polygon? Wait, actually, the figure shown is a concave polygon (or a non - convex, specifically a concave, or a self - intersecting? Wait, no, the standard star polygon or the given figure: let's check the sides. The figure has straight sides, is closed, and when we check the interior angles, some interior angles are greater than 180? Wait, no, actually, the figure is a polygon (closed, straight sides, no curves, vertices connected by sides). Now, for convex vs concave: a convex polygon has all interior angles less than 180° and all diagonals lie inside the polygon. A concave polygon has at least one interior angle greater than 180° or a diagonal that lies outside. The given star - like figure (a concave polygon, specifically a non - convex, or a concave) – wait, actually, the figure is a polygon (closed, straight sides, no crossing sides? Wait, no, the star - like figure (a four - pointed star) has sides that intersect? Wait, no, the given figure: let's see, the figure is a closed figure with 8 sides? Wait, no, the standard four - pointed star (like a square rotated and connected) – actually, the figure is a polygon (closed, made of straight line segments, no curved sides). Now, to check convex or concave: in a convex polygon, any line segment between two vertices lies inside the polygon. In this star - like figure, if we take two vertices that are "opposite" in the star, the line segment between them would pass outside the interior of the star - shaped figure. Also, some interior angles are greater than 180°. So it is a polygon, and it is concave.

Step2: Confirm polygon criteria

The figure is closed, has straight sides (no curves), and the sides meet at vertices. So it satisfies the definition of a polygon. Then, for convexity: since there are interior angles greater than 180° (or diagonals outside the figure), it is concave.

Answer:

The figure is a polygon, and it is concave.