What is a Vertex in Geometry? - Definition & Examples

What is a Vertex in Geometry? - Definition & Examples
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  • 0:00 What Is a Vertex?
  • 1:04 Angles
  • 1:27 Polygons
  • 2:23 3-D Objects
  • 2:58 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 geometry, a vertex is the point where two straight rays or line segments meet. In this lesson, we will go into more detail about where vertices are found in geometry.

What Is a Vertex?

You walk out the front door and go straight to the park. Your best friend leaves her house and also walks on a straight path to get to the park. The point where you two meet and start to catch up with the latest gossip is a vertex.

A vertex is the point where two straight rays or line segments meet. The plural of vertex is vertices. A point is just a location in space, usually shown with a small dot. In geometry, rays and line segments are very different. Rays go on forever in one direction, which is shown with an arrow on one end of the ray. Line segments end and do not go on forever in either direction. This is shown with points on each end of the line segment and no arrows. Now, an intersection in geometry is the point where two lines cross, and lines can go on forever in both directions, which is shown with an arrow on each end. Intersections can also be vertices because the lines are broken up into rays at the point of intersection.


Vertices are commonly used in geometry when dealing with angles. An angle is the measure between the two lines, rays, or segments that meet at a vertex. These two line segments form an angle. For example, an angle that's commonly seen in geometry measures 45 degrees. A degree is a measure of 1/360th of a circle.


Vertices are also seen in polygons. Polygons are two-dimensional objects made up of straight-line segments. Two-dimensional objects have length and width but no depth. Examples of polygons are squares, rectangles, triangles, and octagons. A line by itself would not be considered a polygon because polygons have to be closed, which means each line segment must touch the ends of two other line segments. In order for a polygon to be closed, it must have a least three line segments with no gaps between the segments.

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