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A polygon is a plane shape in which an area is enclosed by straight lines that meet pairwise.

Two lines cannot enclose an area. Either they are parallel and there are two gaps to the area between them or they meet at an angle and there is a gap in the enclosure opposite the angle.

So there must be at least three sides. Now three lines, taken two at a time create three distinct vertices (a triangle). So the least number of vertices is 3.

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Q: Why can't a polygon have only 2 vertices?
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Can a polygon have only 2 vertices?

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