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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.