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.
Answer
A
All sides and all angles in a polygon are congruent.
B
The sides of a polygon are segments that intersect exactly two other segments, one at each endpoint.
C
In a polygon, all segments with a common endpoint are collinear.
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.
Explanation
In a polygon, each side meets the two neighboring sides at its endpoints, so B is true. For a convex polygon, the line containing any side stays along the boundary or outside the polygon, never through its interior; this makes D true. A concave polygon has an inward indentation, so extending at least one side or diagonal can pass through the polygon’s interior, making E true. A is false because polygon sides and angles do not all have to be congruent, and C is false because sides sharing an endpoint generally are not collinear.
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