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. Not all polygons are regular. So this is false.
• Option 2: By the definition of a polygon, each side (segment) intersects exactly two other segments (one at each endpoint). This is true.
• Option 3: In a polygon, segments with a common endpoint (adjacent sides) are not collinear. If they were collinear, it would not form a polygon. So this is false.
• Option 4: For a convex polygon, when sides are extended, the interior of the polygon is not intersected by the extended sides. This is true.
• Option 5: For a concave polygon, the extension of at least one side or diagonal will pass through the interior of the polygon. This is true.

Answer:

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