Video: Polygons in Plane Geometry

True or false? A polygon has the same number of sides as vertices.

01:55

Video Transcript

True or false? A polygon has the same number of sides as vertices.

This sentence has a few important words that we need to make sure we know what they mean. The sides are the line segments that form the polygon. The vertices are the points where the line segments meet.

Let’s look at this hexagon and see what we think. First, we can count the sides: one, two, three, four, five, six. Our example polygon has six sides. And how many vertices? One, two, three, four, five, six. So we think “okay, it’s true in a hexagon.” But our question is asking if it’s true in all polygons. Do all polygons have the same number of sides as vertices?

Here’s a triangle. Triangles have three sides and three vertices, parallelograms four-sided quadrilaterals with four vertices, and a pentagon five sides, five vertices. Are we starting to see a pattern?

When you look at every type of polygon, it always has the same number of sides as vertices. And that means this statement would be true: a polygon has the same number of sides as vertices, true.

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