Question

Which statement is false? Explain.

A. An equiangular polygon has all angles congruent.
B. A regular polygon is both equilateral and equiangular.
C. An equilateral polygon has all sides congruent.
D. A polygon is concave if no diagonal contains points outside the polygon.

Answer 1

Answer: D. A polygon is concave if no diagonal contains points outside the polygon.

Step-by-step explanation:

Choice A is true since "equiangular" means "equal angles"

Choice B is true since all sides are congruent, and all angles are congruent for a regular polygon

Choice C is true. The term "lateral" means "side".

Choice D is false because a convex polygon is one where all possible line segments contained in the polygon do not spill outside the polygon. Put another way, if points A and B are in a convex polygon, then every point on line segment AB is also in the polygon. Concave polygons don't have this feature. It is possible to draw a line segment where it spills outside the concave polygon.