# Definition:Polygon/Vertex

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## Definition

A corner of a polygon is known as a **vertex**.

Thus, in the polygon above, the vertices are $A, B, C, D$ and $E$.

## Also defined as

Euclid, in *The Elements*, uses the term **vertex** to mean *the corner of a polygon furthest up the page from the base.*

In the words of Euclid:

*The***height**of any figure is the perpendicular drawn from the vertex to the base.

(*The Elements*: Book $\text{VI}$: Definition $4$)

## Notation and Terminology

Both the vertices and the sizes of the internal angles of those vertices are frequently referred to by the same symbol.

Thus **the size of the internal angle at vertex $A$** is called **angle $A$** and denoted $\angle A$.

This is considered by some to be an abuse of notation, but its convenience outweighs its disadvantages.

## Also see

## Linguistic Note

The plural of **vertex** is **vertices**.

The word **vertex** is Latin for **peak**, from which the irregular plural form.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**vertex**:**1a.** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**polygon** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**versiera** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**polygon**