A polygon is convex if and only if a segment connecting any two vertices never passes through the exterior of the polygon.If this statement is true, then which of the following statements must also be true?A.A segment connecting any two vertices of a polygon never passes through the exterior of a polygon if and only if the polygon is not convex.B.A polygon is not convex if and only if a segment connecting any two vertices never passes through the exterior of the polygon.C.A polygon is convex if and only if a segment connecting any two vertices never passes through the interior of the polygon.D.A polygon is not convex if and only if a segment connecting any two vertices passes through the exterior of the polygon.

A is the same thing as the statement, only that it says if the polygon is convex. Same thing for B. C could've worked if it said exterior instead of interior. D is basically the converse of the statement.

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ashishdwivedilVT ashishdwivedilVT · Answer 2 · 2022-03-19T08:19:26+01:00

A polygon is not convex if and only if a segment connecting any two vertices passes through the exterior of the polygon i.e option D

What is the difference between a convex polygon and a concave polygon?

Each interior angle of a convex polygon is less than 180° while in the case of the concave polygon at least one angle is more than 180°.

In the diagram attached,

We can see in the case of a convex polygon if we join any two vertices, a line segment joining two vertices never passes through the exterior or interior of the polygon.

In the case of a concave polygon, at least a line segment joining two vertices passes through the exterior of a polygon.

Therefore, A polygon is not convex if and only if a segment connecting any two vertices passes through the exterior of the polygon i.e option D

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