Lesson Video: Polygons and Nonpolygons Mathematics

In this video, we will learn how to identify a polygon among two-dimensional figures.

10:14

Video Transcript

Polygons and Nonpolygons

In this video, we will learn how to identify a polygon among two-dimensional shapes.

Here are some two-dimensional shapes or 2D shapes. How do we know if a 2D shape is a polygon? Polygons have straight sides. The heart shape isn’t a polygon because some of its sides are curved. The circle isn’t a polygon either because it has one curved edge. And the oval isn’t a polygon either. All of these 2D shapes have straight sides. All of these shapes are polygons.

Polygons are also closed shapes. That means that all of the sides are connected. This is a closed shape. All of the sides are connected. If we start at this point here and join all of the sides, eventually, we come back to the point where we started. So all of these 2D shapes are polygons. They’re all closed 2D shapes with straight sides.

Is this shape a polygon? It’s a 2D shape. It’s a closed shape. And it has straight sides. So this shape is a polygon. Is this shape a polygon? This shape has a curved edge. Polygons have straight sides. So this shape is not a polygon. Is this figure a polygon? This figure is open. We know that polygons are closed shapes, so we know that this figure is not a polygon either. We’ve learned that polygons are closed 2D shapes with straight sides. Let’s practice identifying polygons with some questions.

Scarlett has sorted these shapes into polygons and not polygons. Fill in the blank. All polygons are closed and what. Have more than four edges or sides, have curves, or have straight edges or sides.

We know that Scarlett has sorted her shapes into two groups, polygons and not polygons. We’re told that all polygons are closed shapes. We have to pick another statement, which is true. Do all polygons have more than four edges, curves, or straight sides? Let’s check the polygons. Do all of these polygons have more than four edges or sides? No, they don’t. There’s a triangle. We know that triangles have three edges or three sides, so we know the first statement is false.

Do all polygons have curves? None of the polygons have curves. Some of the shapes in the group of not polygons have curves, but none of the polygons have curves. We know that this statement is also false. Do all polygons have straight edges or straight sides? Yes, they do. All of the shapes which Scarlett has sorted into the polygons group have straight sides. We looked closely at the shapes in Scarlett’s groups, the polygons and not polygons. All polygons are closed and have straight edges or straight sides.

Which of these is a polygon?

We’ve learned now that polygons are closed shapes which have straight sides. This is a closed shape and it has straight sides. So this is a polygon. This figure is open. It’s not a polygon. This is a curved shape. So it’s not a polygon either. All polygons are closed and have straight edges. This is the shape which is a polygon.

Is the given shape a polygon?

We know that polygons are closed shapes; the sides are all connected. If we started drawing at the pink dot and drew all the way around the shape, we would come back to the start point. This shape is a closed shape. We also know that polygons have straight sides, and all of the sides of this shape are straight. The given shape is a polygon. So the answer to the question “is the given shape a polygon?” is yes. We know it’s a polygon because it’s a 2D shape. It’s a closed shape. And it has straight sides.

True or false? To draw a polygon, you must draw at least three line segments.

Let’s draw a shape with three line segments. One, two, three. We drew a triangle. This triangle is a polygon. It has three line segments. All of its lines are straight. And it’s a closed shape. Is it possible to draw a polygon which has less than three line segments?

This figure is made from two line segments. Is it a polygon? No, it’s an open shape. We know that polygons are closed shapes. Here’s another figure made from two line segments. This is also an open figure. So to draw a polygon, we need at least three sides or three line segments. The given statement is true. To draw a polygon, you must draw at least three line segments.

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

This shape is a polygon. Does it have the same number of sides as vertices? It has six sides and six vertices. Let’s try a different polygon. This polygon has four sides and four vertices. We drew two polygons. Both had the same number of sides as vertices. The statement is true. A polygon has the same number of sides as vertices.

I want to join two vertices in this shape with a straight line so I can create two new polygons which have the same number of sides. Which vertices could I join? 𝐵 and 𝐹, 𝐴 and 𝐸, 𝐵 and 𝐸, or 𝐴 and 𝐶.

In this question, we have to join two vertices from the given shape with a straight line to create two new polygons which both have the same number of sides. If we join the vertices 𝐵 and 𝐹, we get two new polygons. But do they both have the same number of sides? One of our polygons has three sides. The other has five sides. So we know it’s not 𝐵 and 𝐹.

If we join the two vertices 𝐴 and 𝐸, we get two new polygons. And again, one of our polygons is a triangle with three sides, and the other shape has five sides. One, two, three, four, five. What happens if we join the vertices 𝐵 and 𝐸? We’ve made two new polygons, and it looks like they both have the same number of sides. One, two, three, four. And our second new polygon also has one, two, three, four sides.

If we join the two vertices 𝐵 and 𝐸 in this shape, we can create two new polygons which have the same number of sides. Both have four sides. We joined vertices 𝐵 and 𝐸.

What have we learned in this video? We’ve learned how to identify polygons. And we’ve learned that polygons are closed 2D shapes with straight sides.

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