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

Correct statements: 2, 4, and 5.

Brief reasons:
- 2 is true: each side of a (simple) polygon is a segment that meets exactly two other sides, one at each endpoint.
- 4 is true: in a convex polygon the line containing any side is a supporting line, so it does not pass through any interior point.
- 5 is true: a concave polygon has at least one reflex vertex, so the line containing some side or diagonal will pass through the interior.

Statements 1 and 3 are false (1 is only true for regular polygons; 3 would make angles 180° and not form a polygon).