Question

identify the polygon. if not a polygon, state why.
choose the correct answer below.
a. the figure is a pentagon.
b. the figure is a hexagon.
c. the figure is a heptagon.
d. the figure is not a polygon because there is a \side\ that is a curve and not a line segment.
e. the figure is not a polygon because two sides intersect only one other side.
f. the figure is not a polygon because there is a side that intersects more than two other sides.

Explanation:

A polygon is a closed figure made up of straight line segments. In the given figure, if there is a side that is a curve (not a line segment), it violates the definition of a polygon. Options A - C assume it's a polygon (pentagon, hexagon, heptagon which are all polygons with 5, 6, 7 straight - sided respectively). Option E is incorrect as in a non - polygon with a curved side, the issue is not about the number of sides a side intersects in terms of line - side intersection (in a polygon, each side intersects exactly two other sides at vertices). Option F is also incorrect for the same reason as E; the main deviation from the polygon definition here is the presence of a non - line - segment (curved) side.

Answer:

D. The figure is not a polygon because there is a "side" that is a curve and not a line segment.