Polygons: Symmetry & Vertices

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  • 0:03 What Is a Polygon?
  • 0:55 Vertices
  • 1:27 Symmetry
  • 3:35 Lesson Summary
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Lesson Transcript
Instructor: Stephanie Matalone

Stephanie taught high school science and math and has a Master's Degree in Secondary Education.

In this lesson, we'll go over the basics of what polygons are, specifically focusing on symmetry in polygons and where the vertices can be found. We'll look at examples and images to examine these concepts.


There's no point talking about vertices and symmetry if we don't even know what a polygon is, so let's start there! Polygons are two-dimensional figures made up of a minimum of three straight lines. Polygons can look really different from one another depending on how those lines are oriented, how long they are, and how many there are. The important thing is that the lines are not curved and that the object closes.


In this image, you can see examples of two polygons on the right hand side. These are polygons because they are closed figures made of straight lines. The two figures on the left are not polygons. The image on the top left is not closed, while the image on the bottom left is made of a curved line. You may recognize that bottom figure as a circle, which is not considered to be a polygon.


Vertices are the points where the sides of a polygon meet. The singular form of the word is vertex. A triangle with three sides has three points where its sides meet and, thus, has three vertices.


In this image, you can see a polygon with six sides. This polygon also has six vertices which are marked with red points and labeled with letters. Points A, B, C, D, E, and F are all vertices because two sides of the polygon meet at those points.


You've probably heard the word 'symmetry' before in your life. Sometimes you hear people saying that an individual has a symmetrical face. This means that their face is even, or the same on both sides. Imagine drawing a line down their face from the center of their forehead, through the middle of their nose, and into their chin. Features on each side of this line would be the same, like mirror images of one another.

This same concept can be applied to polygons. Formally, symmetry means that if an object is split in half, those halves are the same. Objects that are symmetrical will have lines of symmetry that split the object into equal halves, just like the line drawn down a face. If you were to fold the object across the line of symmetry, it would fold over exactly, with no parts showing through. In other words, the two halves are mirror images or reflections of one another.


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