Video: Understanding Properties of Polygons

Determine whether the following statement is always, sometimes, or never true: A polygon has more vertices than sides.

03:39

Video Transcript

Determine whether the following statement is always, sometimes, or never true. A polygon has more vertices than sides.

Let’s identify some words we need to know. A vertex, or vertices if there’s more than one, is a place where two sides meet in a flat shape. A side of a polygon is one of the line segments that make up a flat shape. Let’s look at some polygons to try and determine if this statement is true.

Here are five different polygons. Let’s count their vertices and sides and then compare those numbers. We’ll start with the square. The square has one, two, three, four sides. And it has one, two, three, four vertices.

Next up, the rectangle: one, two, three, four sides and the vertices one, two, three, four. Let’s go back and read our statement. Our statement says a polygon has more vertices than sides. In our square and in our rectangle, they both have the same number of sides and vertices. So we cross out the word “always.”

A polygon has more vertices than sides: it can’t be always true, because we’ve already found two examples where it’s not true. On to our last few polygons, this triangle has one, two, three sides and one, two, three vertices, three sides three vertices. And the pentagon one, two, three, four, five sides and one, two, three, four, five vertices.

Are we starting to see a pattern here? We’ll go ahead and check our hexagon and then make a decision about the statement. The hexagon has one, two, three, four, five, six sides and one, two, three, four, five, six vertices.

In these six examples, each polygon has the same number of sides and vertices. They do not have more vertices than sides. In fact, it is never true that a polygon will have more vertices than sides. A polygon always has the same number of vertices and sides. The statement “a polygon has more vertices than sides” is never true.

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