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.

Answer 1

True are: 2, 4, and 5.

- 2 is true: each side is a segment joining two consecutive vertices and meets exactly the two adjacent sides, one at each endpoint.
- 4 is true: for a convex polygon every side’s supporting line has the polygon entirely on one side, so the extended sides do not pass through interior points.
- 5 is true: a concave polygon has at least one reflex vertex (interior angle > 180°), so some side or diagonal’s extension will pass through and thus contain a point of the interior.

Statements 1 and 3 are false.