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 poly

Answer 1

Correct answers: 2, 4, and 5.

Brief justifications:
- 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 lies on a supporting line; the interior lies entirely on one side of that line, so the line through any side contains no interior points.
- 5 is true: a concave polygon has at least one reflex indentation, so there is at least one side or diagonal whose extension passes through the interior of the polygon.

Statements 1 and 3 are false (1 only holds for regular polygons; 3 is generally false — segments sharing a vertex need not be collinear).