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Polygons and Nonpolygons
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In this video, we will learn how to identify a polygon among two-dimensional shapes.
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Here are some two-dimensional shapes or 2D shapes.
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How do we know if a 2D shape is a polygon?
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Polygons have straight sides.
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The heart shape isn’t a polygon because some of its sides are curved.
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The circle isn’t a polygon either because it has one curved edge.
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And the oval isn’t a polygon either.
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All of these 2D shapes have straight sides.
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All of these shapes are polygons.
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Polygons are also closed shapes.
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That means that all of the sides are connected.
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This is a closed shape.
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All of the sides are connected.
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If we start at this point here and join all of the sides, eventually, we come back to the point where we started.
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So all of these 2D shapes are polygons.
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They’re all closed 2D shapes with straight sides.
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Is this shape a polygon?
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It’s a 2D shape.
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It’s a closed shape.
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And it has straight sides.
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So this shape is a polygon.
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Is this shape a polygon?
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This shape has a curved edge.
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Polygons have straight sides.
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So this shape is not a polygon.
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Is this figure a polygon?
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This figure is open.
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We know that polygons are closed shapes, so we know that this figure is not a polygon either.
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We’ve learned that polygons are closed 2D shapes with straight sides.
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Let’s practice identifying polygons with some questions.
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Scarlett has sorted these shapes into polygons and not polygons.
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Fill in the blank.
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All polygons are closed and what.
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Have more than four edges or sides, have curves, or have straight edges or sides.
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We know that Scarlett has sorted her shapes into two groups, polygons and not polygons.
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We’re told that all polygons are closed shapes.
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We have to pick another statement, which is true.
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Do all polygons have more than four edges, curves, or straight sides?
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Let’s check the polygons.
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Do all of these polygons have more than four edges or sides?
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No, they don’t.
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There’s a triangle.
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We know that triangles have three edges or three sides, so we know the first statement is false.
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Do all polygons have curves?
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None of the polygons have curves.
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Some of the shapes in the group of not polygons have curves, but none of the polygons have curves.
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We know that this statement is also false.
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Do all polygons have straight edges or straight sides?
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Yes, they do.
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All of the shapes which Scarlett has sorted into the polygons group have straight sides.
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We looked closely at the shapes in Scarlett’s groups, the polygons and not polygons.
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All polygons are closed and have straight edges or straight sides.
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Which of these is a polygon?
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We’ve learned now that polygons are closed shapes which have straight sides.
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This is a closed shape and it has straight sides.
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So this is a polygon.
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This figure is open.
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It’s not a polygon.
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This is a curved shape.
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So it’s not a polygon either.
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All polygons are closed and have straight edges.
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This is the shape which is a polygon.
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Is the given shape a polygon?
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We know that polygons are closed shapes; the sides are all connected.
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If we started drawing at the pink dot and drew all the way around the shape, we would come back to the start point.
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This shape is a closed shape.
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We also know that polygons have straight sides, and all of the sides of this shape are straight.
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The given shape is a polygon.
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So the answer to the question “is the given shape a polygon?” is yes.
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We know it’s a polygon because it’s a 2D shape.
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It’s a closed shape.
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And it has straight sides.
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True or false?
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To draw a polygon, you must draw at least three line segments.
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Let’s draw a shape with three line segments.
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One, two, three.
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We drew a triangle.
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This triangle is a polygon.
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It has three line segments.
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All of its lines are straight.
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And it’s a closed shape.
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Is it possible to draw a polygon which has less than three line segments?
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This figure is made from two line segments.
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Is it a polygon?
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No, it’s an open shape.
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We know that polygons are closed shapes.
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Here’s another figure made from two line segments.
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This is also an open figure.
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So to draw a polygon, we need at least three sides or three line segments.
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The given statement is true.
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To draw a polygon, you must draw at least three line segments.
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True or false?
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A polygon has the same number of sides as vertices.
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This shape is a polygon.
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Does it have the same number of sides as vertices?
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It has six sides and six vertices.
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Let’s try a different polygon.
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This polygon has four sides and four vertices.
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We drew two polygons.
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Both had the same number of sides as vertices.
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The statement is true.
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A polygon has the same number of sides as vertices.
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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.
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Which vertices could I join?
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𝐵 and 𝐹, 𝐴 and 𝐸, 𝐵 and 𝐸, or 𝐴 and 𝐶.
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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.
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If we join the vertices 𝐵 and 𝐹, we get two new polygons.
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But do they both have the same number of sides?
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One of our polygons has three sides.
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The other has five sides.
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So we know it’s not 𝐵 and 𝐹.
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If we join the two vertices 𝐴 and 𝐸, we get two new polygons.
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And again, one of our polygons is a triangle with three sides, and the other shape has five sides.
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One, two, three, four, five.
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What happens if we join the vertices 𝐵 and 𝐸?
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We’ve made two new polygons, and it looks like they both have the same number of sides.
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One, two, three, four.
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And our second new polygon also has one, two, three, four sides.
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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.
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Both have four sides.
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We joined vertices 𝐵 and 𝐸.
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What have we learned in this video?
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We’ve learned how to identify polygons.
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And we’ve learned that polygons are closed 2D shapes with straight sides.