How to Identify the Vertex of an Angle

Instructor: Artem Cheprasov

Artem has a doctor of veterinary medicine degree.

Are you confused as to what a vertex is? Don't fret. This lesson explains in really simple terms with several different examples how you can easily spot the vertex of an angle.

Corner Safety

When you were little, did your mom and dad ever pad the corners of the walls or some furniture to keep you safe? If they did, they did it for good reason. You could've been climbing about, playing with a toy, and not even watching where you were going. As a result, you could've hit your head right against a sharp corner! And what would've happened? You would've cried, it would've hurt, and you may have had a bruise.

But fear not. This lesson on corners is far less painful and won't leave a nasty mark. That's because we don't have to pad these mathematical corners, ones called vertices.

What Is A Vertex?

A line segment is a line that connect two points. The line segment has a beginning and an end. Think of a 12 inch ruler. It has a definite beginning and a definite end. The beginning starts at 0.00 inches and the end is at 12 inches.

A ray is a bit different. Imagine some measuring tape that extends out as far as the eye can see to the horizon and beyond to infinity. This has a beginning, the plastic box from where the measuring tape unrolls, but it has no end because it extends out to infinity. So unlike a line segment that has a definite beginning and a definite end, a ray has a definite beginning but no end point whatsoever.

What does this have to do with a vertex? Well, a vertex is just the common endpoint of rays and/or line segments. Vertices is the plural form of vertex. One vertex, two or more vertices. Simple as that.


If all of that is giving you a headache, don't worry. You already know what vertices are, you just don't know that's what they're called. Get out a piece of paper and pencil for the rest of this lesson so you can draw some simple shapes to prove that you know what vertices are. Drawing is a lot more fun too!

Draw a square. The square consists of four line segments. The four sharp corners where the line segments meet are called vertices. In other words, each corner is a vertex that connects two line segments at a 90 degree angle.

Now draw a triangle. Any shape or size you want. The triangle is made up of three line segments and three sharp corners. Each corner of that triangle is a vertex. The lines extending away from that vertex form an angle to one another. So each corner is a vertex of an angle.

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