Question

which statements are true about polygons? select three options. all sides and all angles in a polygon are congruent. the sides of a polygon are segments that intersect exactly two other segments, one at each endpoint. in a polygon, all segments with a common endpoint are collinear. if all of the sides of a convex polygon are extended, none of them will contain any points that are inside the polygon. the extension of at least one side or diagonal in a concave polygon will contain a point that is inside the polygon.

Explanation:

• Option 1: Only regular polygons have all sides and angles congruent. So, this statement is false.
• Option 2: By the definition of a polygon, each side (segment) intersects exactly two other segments, one at each endpoint. This statement is true.
• Option 3: In a polygon, segments with a common endpoint (adjacent sides) form an angle, so they are not collinear. This statement is false.
• Option 4: For a convex polygon, when sides are extended, no extended side will pass through the interior of the polygon. This statement is true.
• Option 5: In a concave polygon, the extension of at least one side or diagonal will pass through the interior of the polygon. This statement is true.

Answer:

B. The sides of a polygon are segments that intersect exactly two other segments, one at each endpoint.
D. If all of the sides of a convex polygon are extended, none of them will contain any points that are inside the polygon.
E. The extension of at least one side or diagonal in a concave polygon will contain a point that is inside the polygon.